Contraction Type Research Articles

Common Fixed Point of Generalized Berinde Type Contraction and an Application

In this paper, we introduce $\lambda_{(s,\varphi,\psi,L)}$-generalized Berinde type contraction and obtain some common fixed point results for such class of contractions the setting of triangular $\alpha$-admissible mappings with respect to $\eta$ in the framework of $b$-metric spaces. Our results generalize and extend some theorems in the literature. An example is given to support our result.

The importance of analysing a single common window of a concentric and eccentric dynamic muscle contraction: unveiling the components of EMG data and motor unit pool

This study proposes a method for analysing decomposed electromyographic signals to enhance the characterization of motor units (MU). It involves two steps: (i) clustering groups of motor units based on firing rate (FR), recruitment threshold, and MU action potential amplitude, and (ii) segmentation of data at the time of interest. Such method, capable of distinguishing different groups of MU, could help understanding muscle force production. FR of MU in Vastus Lateralis and Rectus Femoris during knee extension was investigated. The findings distinguish MU groups and reveals differences in: FR between both contractions types; clustered groups; and segmented MU data in both contraction types.

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}-contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}. Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi$$\\end{document} and ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

A narrative review of velocity-based training best practice: The importance of contraction intent vs. movement speed.

Explosive movements requiring high force and power outputs are integral to many sports, posing distinct challenges for the neuromuscular system. Traditional resistance training can improve muscle strength, power, endurance, and range of motion; however, evidence regarding its effects on athletic performance, such as sprint speed, agility, and jump height, remains conflicting. The specificity of resistance training movements, including velocity, contraction type, and joint angles affects performance outcomes, demonstrates advantages when matching training modalities with targeted sports activities. However, independent of movement speed, the intent to contract explosively (ballistic) has also demonstrated high velocity-specific training adaptations. The purpose of this narrative review was to assess the impact of explosive or ballistic contraction intent on velocity-specific training adaptations. Such movement intent may predominantly elicit motor efferent neural adaptations, including motor unit recruitment and rate coding enhancements. Plyometrics, which utilize rapid stretch-shortening cycle (SSC) movements may augment high-speed movement efficiency and muscle activation, possibly leading to improved motor control through adaptations like faster eccentric force absorption, reduced amortization periods, and quicker transitions to explosive concentric contractions. An optimal training paradigm for power and performance enhancement might involve a combination of maximal explosive intent training with heavier loads and plyometric exercises with lighter loads at high velocities. This narrative review synthesizes key literature to answer whether contraction intent or movement speed is more critical for athletic performance enhancement, ultimately advocating for an integrative approach to resistance training tailored for sports-specific explosive action.

The Relationship Between Glabellar Contraction Patterns and Glabellar Muscle Anatomy: A Magnetic Resonance Imaging-based Study.

Glabellar contraction patterns were introduced to the scientific literature to help guide glabellar neuromodulator injection algorithms. However, the relationship between the underlying musculature and its influence on these glabellar contraction patterns is unclear. The aim of this study was to identify via Magnetic Resonance Imaging (MRI) glabellar muscle parameters that display an influence on the distribution of individual glabellar contraction patterns. Thirty-four healthy young individuals of Caucasian Polish descent were investigated (17 women, 17 men) with a mean age of 23.6 years and a mean BMI of 22.8 kg/m2. MRI-based measurements of length, thickness, width and surface area of procerus, corrugator supercilii, orbicularis oculi and frontalis muscles were conducted. Unadjusted models revealed that there was no statistically significant difference between the five glabellar contraction types and the investigated muscle parameters indicating that independent of the skin rhytid pattern, the underlying musculature was not different between the investigated groups in this sample with all p ≥ 0.102. Adjusted models revealed that sex was the most influential factor due to males displayed in general higher values for the investigated parameters when compared to females. The results of this study reveal that based on the MRI parameters investigated and based on the investigated cohort, there does not appear to be a strong relationship between glabellar contraction patterns and underlying glabella muscle anatomy. Utilizing glabellar contraction patterns to design neuromodulator treatment algorithms may be of variable clinical merit.

Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.

Efficacy of lower limb strengthening exercises based on different muscle contraction characteristics for knee osteoarthritis: a systematic review and network meta-analysis.

While strengthening exercises are recommended for knee osteoarthritis (KOA) treatment, the optimal type of muscle contraction remains unclear, with current research showing conflicting results. This network meta-analysis (NMA) aims to evaluate the efficacy of lower limb strengthening exercises based on different muscle contraction characteristics for KOA patients and provide clinical references. We conducted the NMA following the PRISMA-NMA. A comprehensive search of five databases (PubMed, Web of Science, CENTRAL, Embase, and SPORTDiscus) up to August 2024 identified randomized controlled trials (RCTs) investigating lower limb strengthening exercises in KOA patients. Control groups included receiving usual care, only providing health education, or no intervention at all. Outcomes analyzed included pain, physical function, quality of life, and muscle strength. Forty-one studies (2,251 participants) were included. Twenty-eight studies used rigorous randomization; eighteen reported allocation concealment. All had high performance bias risk due to exercise interventions. Regarding efficacy, isokinetic exercise ranked highest in pain relief (SMD = 0.70, 95% CI: 0.50-0.91, SUCRA = 82.6%), function improvement (SMD = 0.75, 95% CI: 0.57-0.92, SUCRA = 96.1%), and enhancement in muscle strength (SMD = 0.56, 95% CI: 0.34-0.78, SUCRA = 90.1%). Isometric exercise ranked highest in improving quality of life (SMD = 0.80, 95% CI: 0.28-1.31, SUCRA = 90.5%). Mixed strengthening exercise ranked lowest across all outcomes. High-frequency interventions (≥5 times/week) showed superior pain relief compared with low-frequency (≤3 times/week) for isotonic, isometric, and isokinetic exercise. This NMA suggests isokinetic exercise may be most effective for pain, function, and muscle strength in KOA patients, while isometric exercise benefits quality of life most. Mixed strengthening exercise ranked lowest across all outcomes. High-frequency interventions appear more effective than low-frequency ones. These findings support personalized KOA treatment, considering efficacy, accessibility, and patient-specific factors. Study biases, heterogeneity, and other limitations may affect result reliability. Future research should focus on high-quality studies with standardized protocols and analyze dose-response relationships to refine KOA treatment strategies. https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42024582525, identifier: CRD42024582525.

A Fixed Point Theorem for Non-Self Mappings of Rational Type in 𝔟−Multiplicative Metric Spaces with Application to Integral Equations

Objectives: To prove fixed point theorem for non-self mappings of rational type in -multiplicative metric spaces and apply the theorem to solve integral equations. Method: Multiplicative metrically convex is defined in the context of - multiplicative metric spaces to prove fixed point theorems for pairs of non-self mappings using rational type contraction. Findings: The theorem demonstrates that under certain rational type contraction, a unique fixed point exists for non-self mappings in -multiplicative metric spaces. Applications of integral equations shown improved convergence and solution accuracy. Novelty: First fixed point theorem for non-self mappings in -multiplicative metric spaces, introducing a new approach to solving Volterra-Hammerstein integral equations. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: Coincidence Point, Nonself Mappings, Rational Type contraction, b-Multiplicative Metric Spaces (b-m ́ms), Volterra-Hammerstein integral equations

Super Metric Space and Fixed Point Results

Banach contraction principle is the beginning of the Metric fixed point theory. This principle gives existence and uniqueness of fixed points and methods for obtaining approximate fixed points. It is the basic tool of finding fixed points of all contraction type maps. It has a constructive proof which makes the theorem worthy because it yields an algorithm for computing a fixed point. Banach fixed point result has been extended by various authors in many directions either by weakening the conditions of contraction mapping or by changing the abstract structure. Several generalizations and extensions of metric spaces have been introduced. Among these, the prominent extensions are b-metric space, fuzzy metric space, partial metric space and a lot more of their combinations. In particular, a new structure namely Super metric space is introduced. In the present paper, we generalize and extend the fixed point results of fixed point theory in literature in the framework of super metric space.

Extension of Meir-Keeler-Khan (ψ − α) Type Contraction in Partial Metric Space

In numerous scientific and engineering domains, fractional-order derivatives and integral operators are frequently used to represent many complex phenomena. They also have numerous practical applications in the area of fixed point iteration. In this article, we introduce the notion of generalized Meir-Keeler-Khan-Rational type (ψ−α)-contraction mapping and propose fixed point results in partial metric spaces. Our proposed results extend, unify, and generalize existing findings in the literature. In regards to applicability, we provide evidence for the existence of a solution for the fractional-order differential operator. In addition, the solution of the integral equation and its uniqueness are also discussed. Finally, we conclude that our results are superior and generalized as compared to the existing ones.

Some results related to common fixed point of four maps in f-metric spaces

The purpose of this paper is to present some existence and uniqueness results for some common fixed points of four mappings in F-metric spaces that satisfy the generalized conditions. Whereas, the new proposed two theorems allow to generalize and improve some theorems published in many previous papers related to fixed point in F-metric spaces. Indeed, the basics of the two new theorems proposed in this paper include a generalization and improvement of the previous well-known theorems in metric space, F-metric space and class of F-metric spaces, leading to more flexibility in their understanding and their applications. Furthermore, the proposed theorems allow overcoming the weak contraction type faced in the common fixed point theorem in the setting of F-metric spaces. Some examples are presented to prove that the proposed theorems are complementary and applicable where the existence and uniqueness of common fixed points of four mappings in F-metric spaces in the form of integrals are obtained.

([formula omitted])-contractive and ([formula omitted])-contractive mapping based fixed point theorems in fuzzy bipolar metric spaces and application to nonlinear Volterra integral equations

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely (αη)-contractive type covariant mappings and contravariant mappings, and (βχ)-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for (αη)-contractive type covariant mappings and contravariant mappings, and for (βχ)-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of (αη)-contractive mappings and (βχ)-contractive mappings in this domain.

Fixed-Point Theorems Using α-Series in F-Metric Spaces

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using α-series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation.

Intracerebroventricular insulin injection acutely normalizes the augmented exercise pressor reflex in male rats with type 2 diabetes mellitus.

The exercise pressor reflex (EPR) is exaggerated in type 2 diabetes mellitus (T2DM), but the underlying central nervous system aberrations have not been fully delineated. Stimulation of muscle afferents within working skeletal muscle activates the EPR, by sending information to neurons in the brainstem, where it is integrated and results in reflexively increased mean arterial pressure (MAP) and sympathetic nerve activity. Brain insulin is known to regulate neural activity within the brainstem. We hypothesize that brain insulin injection in T2DM rats attenuates the augmented EPR, and that T2DM is associated with decreased brain insulin. Using male Sprague-Dawley rats, T2DM and control rats were generated via an induction protocol with two low doses of streptozotocin (35 and 25mg/kg, i.p.) in combination with a 14-23-week high-fat diet or saline injections and a low-fat diet, respectively. After decerebration, MAP and renal sympathetic nerve activity (RSNA) were evaluated during EPR stimulation, evoked by electrically induced muscle contraction via ventral root stimulation, before and after (1 and 2h post) intracerebroventricular (i.c.v.) insulin microinjections (500mU, 50nl). i.c.v. insulin decreased peak MAP (ΔMAP Pre (36±14mmHg) vs. 1h (21±14mmHg) vs. 2h (11±6mmHg), P<0.05) and RSNA (ΔRSNA Pre (107.5±40%), vs. 1h (75.4±46%) vs. 2h (51±35%), P<0.05) responses in T2DM, but not controls. In T2DM rats, cerebrospinal fluid insulin was decreased (0.41±0.19 vs. 0.11±0.05ng/ml, control (n=14) vs. T2DM (n=4), P<0.01). The results demonstrated that insulin injections into the brain normalized the augmented EPR in brain hypoinsulinaemic T2DM rats, indicating that the EPR can be regulated by brain insulin. KEY POINTS: The reflexive increase in blood pressure and sympathetic nerve activity mediated by the autonomic nervous system during muscle contractions is also known as the exercise pressor reflex. The exercise pressor reflex is dangerously augmented in type 2 diabetes, in both rats and humans. In type 2 diabetic rats both cerebrospinal fluid insulin and phosphoinositide 3-kinase signalling within cardiovascular brainstem neurons decrease in parallel. Brain insulin injections decrease the magnitude of the reflexive pressor and sympathetic responses to hindlimb muscle contraction in type 2 diabetic rats. Partial correction of low insulin within the central nervous system in type 2 diabetes may treat aberrant exercise pressor reflex function.

Certain Fixed Point Results via Contraction Mappings in Neutrosophic Semi-Metric Spaces

In this work, the authors introduce the concept of neutrosophic semi-metric spaces and prove several common fixed-point theorems for countable and uncountable family of mappings via an implicit relation of contractive and integral type by utilizing locally integrable functions. These results improve and generalize the several results in the existing literature. Further, the authors present some non-trivial examples to support our main results. Mathematics Subject Classification: 46S40, 47H10, 54H25.

A Comparison of the Plyometric Performance of Upper Limbs between Experienced and Non-Experienced Athletes.

Although explosive upper-limb movements are far less studied than the equivalent lower-limb movements, they are important in many sports activities. The goal of this study was to explore, for the first time, the performance of street workout (SW) athletes who primarily focus on explosive and isometric strength in the upper limbs and to examine the effect of the contraction type on performance during a classical upper-body movement. Eighteen men took part in this study (age: 22.6 ± 2.1 years, height: 179.6 ± 7.1 cm, bodyweight: 71.9 ± 6.6 kg). Of these, nine practiced SW and nine practiced various team and individual sports-the latter serving as the control group. The athletes performed three different types of push-ups-one in a concentric way and two others in a plyometric way-and a fatigue-inducing push-up set. Jump heights, myoelectrical activities (through electromyography), muscle architecture, and hypertrophy (through ultrasonography) were measured. The results show no significant differences in jump height between the push-up types. Both groups confounded, but the SW athletes jumped on average 66 ± 21% higher than the control athletes (p < 0.05). There was no major difference in EMG between groups, regardless of the push-up type, but the SW athletes had a greater pectoralis major and anterior deltoid thickness as well as a greater pennation angle of the pectoralis major. The results suggest that the plyometric performance of the upper limbs does not follow the same pattern as that of the lower limbs. The SW group's greater capacity in performing explosive push-ups could be attributed to greater upper-body muscle hypertrophy and more efficient execution of the movement.

Fixed Point Results for Geraghty Type Contractions in Extended Rec-tangular Fuzzy &lt;i&gt;b&lt;/i&gt;-metric Space with an Application

The aim of this paper is to define the notions of extended fuzzy b-metric spaces, fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces and to establish certain fixed point results in these settings utilizing Geraghty type contractions. We also furnished an example which illustrates our main result. To show the authenticity of our results we provide an application involving fuzzy integral equation. The obtained results generalize many existing results in the literature.

Unlocking the benefit of active stretch: the eccentric muscle action, not the preload, maximizes muscle-tendon unit stretch-shortening cycle performance.

Stretch-shortening cycles (SSCs) outperform shortening contractions preceded by isometric contractions in terms of enhanced force/torque, work, and power production during shortening. This so-called SSC effect is presumably related to the active muscle stretch before shortening in SSCs. However, it remains unclear whether the effects of stretch-induced higher preload level or stretch-induced history dependence maximize the SSC effect. Therefore, we analyzed fascicle behavior, muscle-tendon unit (MTU) shortening work, and torque/force (n = 12 participants) via ultrasound and dynamometry during electrically stimulated submaximal plantar flexion contractions from 10° plantarflexion to 15° dorsiflexion. To elucidate the effects of preload level and preload modality (i.e., contraction type) on shortening performance, muscle-tendon unit shortening was preceded by fixed-end (SHO), active stretch (SSC), and preload-matched fixed-end (MATCHED) contractions. Before shortening, MATCHED and SCC had the same preload level (1% torque difference), similar joint position, and muscle fascicle lengths. Compared with SHO, shortening work was significantly (P < 0.001, partial η2 = 0.749) increased by 85% and 55% for SSC and MATCHED, respectively, with SSC shortening work being significantly higher than MATCHED (P = 0.016). This indicates that preload contributes by 65% to the overall SSC effect so that 35% needs to be referred to stretched-induced history-dependent mechanisms. In addition, SSC showed larger fascicle forces at the end of shortening (P < 0.001) and 20% less depressed isometric torque following shortening compared with MATCHED (P < 0.001). As potential decoupling effects by the series elastic element were controlled by matching the preload levels, we conclude that the difference between SSC and MATCHED is related to stretch-induced long-lasting history-dependent effects.NEW & NOTEWORTHY Using a torque-matched preload protocol, we found that 2/3 of the performance enhancement in muscle-tendon unit stretch-shortening cycles (SSCs) is caused by the increased preload level. The remaining 1/3 is owed to the long-lasting history-dependent effects triggered during the stretch in SSCs. This increased performance output is attributed to passive elastic structures within the contractile element that do not require additional muscle activation, therefore contributing to the higher efficiency of the neuromuscular system in SSCs.

Can the efficacy of a medical treatment be predicted based on the type of idiopathic premature ventricular contraction?

BackgroundPremature ventricular contractions (PVCs) are common arrhythmias with diverse clinical implications. This retrospective study aimed to evaluate the efficacy of medical treatments using various clinical, imaging, and electrocardiographic parameters in patients with idiopathic PVCs. MethodsA total of 1051 patients with idiopathic PVCs were retrospectively analyzed. Patients were categorized into three groups based on treatment response: beta-blocker (BB) responders (479 patients), calcium-channel blocker (CCB) responders (335 patients), and class 1c antiarrhythmic (AA) responders (237 patients). Clinical, imaging, and electrocardiographic data were collected and analyzed to assess the factors influencing treatment response. ResultsAge, left ventricular ejection fraction (LVEF), PVC QRS duration, CI variability, and multiple PVC morphologies were identified as significant factors affecting treatment response. Older age and lower LVEF were associated with better response to BB treatment, whereas CCB responders showed narrower QRS complexes. BB responders also exhibited higher CI variability, possibly linked to automaticity mechanisms. Moreover, the BB responder group had a higher frequency of multiple PVC morphologies. ConclusionThese findings emphasize the importance of tailored treatment approaches based on individual patient characteristics.

Reliability of cervicocephalic sense of force

Cervicocephalic proprioception (CCP) is an important assessment item for people with a range of clinical conditions, where reduced CCP is associated with neck pain and imbalance. Reliability has been established for a range of positional and movements tests, but there is limited data regarding sense of force, particularly across three planes of movement. The current test–retest study assessed reliability when evaluating sense of force in healthy adults (8 males, 6 females, mean age 31.50 years [SD 10.14]) over two sessions, 4–7 days apart. A force matching protocol was used to evaluate reliability of absolute error (AE), constant error (CE), and variable error (VE) for 10 % and 25 % maximal voluntary contraction (MVC) target forces for flexion, extension, lateral flexion, and rotation. Participants were strapped to a chair to limit trunk movement and data was captured using a compressive force transducer fixed to an adjustable wall mount. Six trials were performed for each contraction-type, totaling 72 submaximal MVCs per session. ICC estimates for AE (0.15–0.77), CE (0.01–0.85), and VE (0.00–0.83) were varied and confidence intervals were mostly wide. Considering lower limits of confidence intervals, CE had best reliability values generally, but more specifically the most reliable contraction type and movement was 25 % MVC flexion (ICC 0.85, confidence interval 0.54–0.95). This study found that reliability for sense of force testing was dependent upon contraction, type of error, and target force utilized. Further reliability analysis should be performed when applying this test to measure validity outcomes in clinical populations.