Weak Contraction Research Articles

On the Family of Theorems on Metric Completeness

There have appeared a large family of theorems related the metric completeness. They are mainly concerned with generalizations of the Banach contraction on quasi-metric spaces and their extended artificial spaces. In this survey article, we classify the family according to our 2023 Metatheorem. Many known metric fixed point theorems belong to the family including the Rus-Hicks-Rhoades (RHR) theorem. Such results on metric spaces are consequences of our generalized forms of the Banach contraction principle for weak contractions or the RHR maps on quasi-metric spaces. We list a large number of examples of metric fixed point theorems which follow from our principles. Moreover, we add some comments on related papers in order to improve them.

Abnormal Uterine Action

The uterus has three distinct layers the endometrium, myometrium, and perimetrium each playing a crucial role in the labour process. The transition from the latent to the active phase of labour is marked by an increase in the intensity and duration of contractions, with shorter intervals between them. Abnormal uterine actions can significantly contribute to dystocia, or difficult labor.T here is two main types of abnormal uterine activity that can lead to complications:  Hypotonic Uterine Activity: This occurs when the resting tone of the uterine muscle is low, resulting in weak or infrequent contractions. This can delay labour progress and may necessitate interventions.  Hypertonic Uterine Activity: In this case, the uterine muscle tone is elevated, leading to frequent but ineffective contractions. This can result in prolonged labour and increased maternal discomfort. Both conditions can confuse the progression of labour and may require careful management to ensure a safe delivery. Effective monitoring and interventions can help address these issues and improve labour outcomes.

Disquisition on convergence, stability, and data dependence for a new fast iterative process

This paper introduces a novel fast iterative process designed for approximating fixed points of contraction and weak contraction mappings. The study presents strong convergence results for this newly proposed iterative process, and proving its efficiency. Analytical and numerical evidences are provided to establish that the proposed iterative method converges more rapidly than several existing processes. Furthermore, stability results and dependence analysis are presented for the newly developed iterative process, enhancing its practical applicability and robustness.

FIXED POINT THEOREMS FOR (ψ, ϕ, ω)-WEAK CONTRACTIONS IN COMPLETE METRIC SPACES

In this paper, we define the mapping called (ψ, ϕ, ω)-weak contractions. We then use this definition to proof the existence of fixed point. The mapping we defined above is a modified mapping by Liu and Chai. We use the concept ω-distance to proof the fixed point theorem. Since every ω-distance is metric, then the resulting theorem also satisfy for every metric.

Weak Contraction for Coupled Fixed Point using Q- Function

Weak Contraction for Coupled Fixed Point using Q- Function

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.

On Certain Fixed Points for (α,φ,F)-Contraction on S_b- Metric Spaces with Applications

This work establishes unique fixed point theorems (UFPT) for self mapping in complete S_b-metric spaces (S_b-MS) with the concept of (α,φ,F)-contraction in the context of S_b-MS Furthermore, we show how the results may be used and present applications to integral equations and homotopy theory. Introduction: In previous work authors were discussed fixed pointon various metric spaces with F -contractions, α-type almost -F- contractions, α-type F -Suzuki contractions, (φ, F)-contraction, F - weak contractions, α −ψ-contractive type, α −ψ-Meir-Keeler contractive mapping, α-ratonal contractive mappings, (α, β) − (φ,ψ)-rational contractive type mappings. Objectives: Finding the unique fixed point for self mapping in S_b-MS, via (α,φ,F)-contraction. Methods: with the help of α- admisible mapping, (φ, F)-contraction, α type F -contraction and (α.φ,F)-contraction we have fixed point findings in complete S_b-metric spaces. Results: we obtained unique fixed point results via (α,φ,F) contractive type for self mapping in complete S_b-MS. Conclusions: In this article, Contractive mappings of the (α,φ,F) type are used to show certain fixedpoint results in the context of S_b-MS, along with appropriate example that illustrate the key findings. Appications to integral equations and homotopy are also offered.

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.

Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation

In this study, we focus on demonstrating the stability of the three-step Z-iterative scheme within the context of weak contraction mappings as defined by Berinde. Further, we attain results concerning stability, data dependence, and error accumulation of the Z-iterative scheme. This article also includes a comparison of the convergence rates among various established iterative strategies. Several illustrative numerical examples are furnished to validate the accuracy and reliability of our findings. In the same spirit, we present an application that utilises the Z-iterative technique on Banach spaces to attain the solution of a delay Caputo fractional differential equation, building upon our primary findings.

Coincidence Points Under Weak Contractions on Symmetric Spaces

Coincidence Points Under Weak Contractions on Symmetric Spaces

Analysis of Factors Affecting the Implementation of Uterine Exploration at the Third Stage of Labor

Labor is one of the critical periods for women based on IDHS data up to 2020 shows that bleeding, hypertension in pregnancy, and infection are the causes of maternal death. Observation data was conducted in January-February 2022 at 5 Puskesmas in the city of Tasikmalaya, and it was found that 3 out of 5 women in labor underwent exploratory procedures during the third stage of labor because there were signs of retained placenta. The act of uterus exploration could be a portal of bacterial entry into the cavity and cause infection. This study aimed to look at the factors that affect the implementation of uterine exploration in the third stage of labor. The research method uses a sequential explanatory mix method to analyze the supporting factors for third-stage exploration actions by midwives. The research sample was 43 midwives. Quantitative results showed that there was no influence of characteristic factors on exploration actions (ρ more than 0.05), and there was no influence of self-efficacy on uterus exploration (ρ more than 0.05). Qualitative results showed that there were four main factors supporting exploration, such as visible signs of bleeding and weak contractions, ensuring that there were no remaining placentas and routine actions that were carried out. The research concludes that the exploratory action carried out is the midwife's accumulated experience, which results in the perception of dealing with cases of retained placenta in the third stage of labor, this makes the uterus exploration an additional action to anticipate problems.

Perineoplasty for anal incontinence after obstetric anal sphincter injury repair: a case report

BackgroundThe rectal and vaginal walls are typically sutured if severe perineal lacerations with rectal mucosal damage occur during vaginal delivery. In case of anal incontinence after the repair, re-suturing of the anal sphincter muscle is standard procedure. However, this procedure may not result in sufficient improvement of function.Case presentationA 41-year-old woman underwent suture repair of the vaginal and rectal walls for fourth-degree perineal laceration at delivery. She was referred to our department after complaining of flatus and fecal incontinence. Her Wexner score was 15 points. Examination revealed decreased anal tonus and weak contractions on the ventral side. We diagnosed anal incontinence due to sphincter dysfunction after repair of a perineal laceration at delivery. We subsequently performed sphincter re-suturing with perineoplasty to restructure the perineal body by suturing the fascia located lateral to the perineal body and running in a ventral–dorsal direction, which filled the space between the anus and vagina and increased anal tonus. One month after surgery, the symptoms of anal incontinence disappeared (the Wexner score lowered to 0 points), and the anorectal manometry values increased compared to the preoperative values. According to recent reports on the anatomy of the female perineal region, bulbospongiosus muscle in women does not move toward the midline to attach to the perineal body, as has been previously believed. Instead, it attaches to the ipsilateral surface of the external anal sphincter. We consider the fascia lateral to the perineal body to be the fascia of the bulbospongiosus muscle.ConclusionsIn a case of postpartum anal incontinence due to sphincter dysfunction after repair of severe perineal laceration, perineoplasty with re-suturing an anal sphincter muscle resulted in improvement in anal sphincter function. Compared to conventional simple suture repair of the rectal wall only, this surgical technique may improve sphincter function to a greater degree.

Characterizing Mitochondrial Maturation in the Heart

Cardiovascular disease is the leading cause of death around the world and the burden is projected to become worse. Because of their ability to supplant the heart’s weak regenerative capabilities, stem cells and their derivatives have been investigated as a potential therapy. However, stem cell-derived cardiomyocytes are less mature than the cells they would be replacing in a clinical setting, causing many functional shortcomings such as unorganized and weak contraction. An in-depth study of how maturation normally occurs is necessary to identify targets to enhance it. As one of the best-known aspects of cardiomyocyte maturation, the mitochondria, and their substrate preferences, dictate the amount of energy a cell produces as well as modulate a cell’s contraction, differentiation, and survival. Similar to the cell itself, the mitochondria mature over time. However, to what extent mitochondrial maturation drives cardiomyocyte maturation is not clear. In this study, we used mass spectrometry to identify the developmental changes across normal cardiac maturation in mitochondria from mice. We detail key shifts in the mitochondrial proteome over time and identify possible regulators of mitochondrial and cardiomyocyte maturation. Pathway and transcription factor analyses highlight transitions over time to more organized, productive mitochondria. Mechanistic evaluation of identified pathways might reveal current bottlenecks for complete maturation of stem cell-derived cardiomyocytes. This work was supported by RMM091621DS008, NIH155993, and NIH160665. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Public enforcement and corporate maturity mismatch

AbstractThe root of corporate maturity mismatch in developing economies may dwell in the fact that weak contract enforcement capacities suppress financial intermediates' willingness to supply long‐term credit. This study examines the impact of improvements in the legal enforcement environment on corporate maturity mismatch, focusing on the unique setting of China's free trade zones. Using data from non‐financial listed companies between 2010 and 2021, the study investigates how the establishment of FTZs, which signifies an improvement in contract enforcement efficiency, influences firms' financing decisions and maturity mismatch. We find that improvements in the contract enforcement environment significantly discipline the behavior of raising short‐term debt for long‐term investments. The effect is more pronounced for small‐to‐medium‐sized enterprises and non‐state‐owned enterprises, suggesting that such improvements alleviate ownership and size discrimination faced by firms. Mechanism test reveals that access to long‐term loans is the core mechanism. Besides, improvements in public enforcement reduce business risk and enhance firm performance. Strengthening the legal enforcement environment serves as a critical determinant to mitigate corporate maturity mismatch and foster sustained economic development.

Fixed Point Dynamics in a New Type of Contraction in b-Metric Spaces

Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the “open” balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity.

Added load increases the peak frequency of intermuscular coherence

Cortical motor neuron activity appears to drive lower motor neurons through two distinct frequency bands: the β range (15–30 Hz) during weak muscle contractions and γ range (30–50 Hz) during strong contractions. It is unknown whether the frequency of cortical drive shifts continuously or abruptly between the β and γ frequency bands as contraction strength changes. Intermuscular coherence (IMC) between synergistic arm muscles was used to assess how the frequency of common neuronal drive shifts with increasing contraction strength. Muscle activity was recorded by surface electromyography (EMG) from the biceps and brachioradialis in nine healthy adults performing 30-second isometric holds with added loads. IMC was calculated across the two muscle groups during the isometric contraction. Significant IMC was present in the 20 to 50 Hz range with all loads. Repeated measures ANOVA show the peak frequency of IMC increased significantly when load was added, from a peak of 32.7 Hz with no added load, to 35.3 Hz, 35.7 Hz, and 36.3 Hz with three-, five-, and ten-pound loads respectively. An increase in IMC frequency occurs in response to added load, suggesting that cortical drive functions over a range of frequencies as a function of an isometric contraction against load.

On (φ,ψ)-generalized weak contractions in quasi- normed spaces

We propose the definition of quasi-n-normed spaces and prove some new results on fixed points theory related to weak contractions in this framework. We prove the existence and uniqueness of fixed point for (φ,ψ)-generalized weak contractions and (φ,ψ)-generalized weak C-contractions in quasi n-normed spaces. The obtained results extend some known theorems for nonlinear contractive functions on quasi n-normed spaces. In addition, we demonstrate an application of obtained results to Integral Equation.

Fixed Point Methodologies for Orthogonal (Π , ξ )-Weak Contraction Mappings in Orthogonal Branciari Metric Spaces with Applications

Fixed Point Methodologies for Orthogonal (Π , ξ )-Weak Contraction Mappings in Orthogonal Branciari Metric Spaces with Applications

Approximating fixed points of weak enriched contractions using Kirk’s iteration scheme of higher order

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{F}$\\end{document}-contraction, weak enriched F′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{F^{\\prime}}$\\end{document}-contraction, and k-fold averaged mapping based on Kirk’s iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk’s iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature.

Convergence and stability of a novel iterative algorithm for weak contraction in banach spaces

Convergence and stability of a novel iterative algorithm for weak contraction in banach spaces