Weak Contraction Research Articles

Coincidence point theorems for generalized cyclic ( κ h , φ L ) S -weak contractions in partially ordered Menger PM-spaces

In this paper, we introduce a new concept of generalized cyclic (κh, ϕL)S-weak contraction mappings and establish some coincidence point results for such mappings in complete partially ordered Menger PM-spaces. Our results generalize the main results of Nashine (Nonlinear Anal. 75:6160-6169, 2012) and Gopal et al. (Appl. Math. Comput. 233:955-967, 2014). We also obtain the corresponding coincidence point theorems for generalized cyclic (κh, ϕL)S-weak contractions in partially ordered metric spaces. MSC: 47H10; 54H25

A generalization on weak contractions in partially ordered b-metric spaces and its application to quadratic integral equations

AbstractWe introduce the notion of almost generalized(ψ,φ,L)-contractive mappings, and establish the coincidence and common fixed point results for this class of mappings in partially ordered completeb-metric spaces. Our results extend and improve several known results from the context of ordered metric spaces to the setting of orderedb-metric spaces. As an application, we prove the existence of a unique solution to a class of nonlinear quadratic integral equations.

Common Fixed-Point Theorems for Nonlinear Weakly Contractive Mappings

Some common fixed-point results for mappings satisfying a nonlinear weak contraction condition within the framework of ordered metric spaces are obtained. The accumulated results generalize and extend several comparable results well-known from the literature.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

Abstract This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms T n : A n → B n for n ∈ Z 0 + and T : ⋃ j ∈ Z 0 + A 0 j → ⋃ j ∈ Z 0 + B 0 j , or T : A → ( ⋃ B n ) , subject to T ( A 0 n ) ⊆ B 0 n and T n ( A n ) ⊆ B n , such that T n converges uniformly to T, and the distances D n = d ( A n , B n ) are iteration-dependent, where A 0 n , A n , B 0 n and B n are non-empty subsets of X, for n ∈ Z 0 + , where ( X , d ) is a metric space, provided that the set-theoretic limit of the sequences of closed sets { A n } and { B n } exist as n → ∞ and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical identification of dynamic systems.

Dissecting mechanisms behind force control in humans by a mixture of experimentation, mathematical analysis and computer simulations of neuronal models.

Dissecting mechanisms behind force control in humans by a mixture of experimentation, mathematical analysis and computer simulations of neuronal models.

Diminished hERG K+ channel activity facilitates strong human labour contractions but is dysregulated in obese women.

Human ether-a-go-go-related gene (hERG) potassium channels determine cardiac action potential and contraction duration. Human uterine contractions are underpinned by an action potential that also possesses an initial spike followed by prolonged depolarization. Here we show that hERG channel proteins (α-conducting and β-inhibitory subunits) and hERG currents exist in isolated patch-clamped human myometrial cells. We show that hERG channel activity suppresses contraction amplitude and duration before labour, thereby facilitating quiescence. During established labour, expression of β-inhibitory protein is markedly enhanced, resulting in reduced hERG activity that is associated with an increased duration of uterine action potentials and contractions. Thus, changes in hERG channel activity contribute to electrophysiological mechanisms that produce contractions during labour. We also demonstrate that this system fails in women with elevated BMI, who have enhanced hERG activity as a result of low β-inhibitory protein expression, which likely contributes to the weak contractions and poor labour outcomes observed in many obese women necessitating caesarean delivery.

A fixed point theorem for (φ,L )-weak contraction mappings on a partial metric space

In this paper, we explore (\(\varphi,L\))-weak contractions of Berinde by obtaining Suzuki-type fixed point results. Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a 0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and generalize several related results from the literature.

Coupled Fixed Point Results For Mappings Involving (α,ψ) - Weak Contractions In Ordered Metric Spaces And Applications

In this paper we introduce the notion of \((\alpha , \psi)\)- weak contractions and use the notion to establish the existence and uniqueness of coupled common fixed points for the mixed monotone operators in partially ordered metric spaces. The obtained results extend, improve, complement and unify many recent coupled fixed point results present in the literature. The theoretic results are accompanied with suitable examples. An application to the existence and uniqueness of the solution of the system of integral equations is also presented.

Mo1596 High Resolution Manometric Predictors of Post-Fundoplication Dysphagia

INTRODUCTION Post-fundoplication dysphagia is a well-described side effect of antireflux surgery. Esophageal manometry is a standard part of the preoperative evaluation prior to antireflux surgery. However, controversy exists regarding the value of traditional manometry to predict post-operative dysphagia after fundoplication. Today, high-resolution manometry (HRM) has replaced traditional water perfused systems for the analysis of esophageal physiology. The aim of this study was to evaluate the utility of HRM in predicting post-operative dysphagia in patients with an otherwise functioning Nissen fundoplication. METHODS Patients who underwent a laparoscopic Nissen fundoplication at a single institution were identified through a prospectively collected database. Patients were asked to undergo routine post-operative testing 6-12 months after surgery. Patients who had normal post-operative 24-hour pH test scores were eligible for the study. Of these patients, those without available raw data from preoperative HRM were excluded. Traditional ineffective motility (IEM) was defined as mean distal esophageal contraction amplitude of <30mmHg or 30% or less peristaltic waves. Post-operative dysphagia was graded using a standard scoring system (0= never, 1=1-2 times a month, 2=1-2 times per week, 3=daily). A symptom score of 2-3 was used to define post-operative dysphagia. Regression and association analysis of pre-operative manometric risk-factors were performed to determine predictors of post-operative dysphagia. P-values <0.05 were considered significant. RESULTS 95 patients (41 male; 54 female) were included in the analysis. Mean post-operative length of follow up was 14.9 months (range: 2-73). 70.2% patients had normal scores on all HRM parameters. Any dysphagia was reported by 50% of patients (17% grade-1, 23.4% grade-2, and 9.5% grade-3) Nineteen patients had traditional IEM. Of those with dysphagia, one also had traditional IEM. On univariate analysis only distal latency (DL) was found to be a significant predictor (p<0.001) of grade-3 but not grade-2 dysphagia. On multivariate analysis, no preoperative factors were found to be significant predictors of grade-3 dysphagia, but contraction front velocity predicted grade2 dysphagia. CONCLUSION Persistent daily dysphagia occurs in ~10% of patients following an otherwise successful Nissen fundoplication. Advancements in manometric technology provide additional data points in the preoperative analysis of these patients. This analysis reveals that elevated integrated relaxation pressure (IRP) is a useful new metric to predict post-operative dysphagia in addition to traditional identification of weak distal esophageal contraction amplitudes. Pre-operative factors as predictors of post-fundoplication dysphagia

Mo1597 Impedance Planimetry as a Diagnostic Tool to Evaluate the Degree of Clinical Lower Esophageal Sphincter Dysfunction

INTRODUCTION Post-fundoplication dysphagia is a well-described side effect of antireflux surgery. Esophageal manometry is a standard part of the preoperative evaluation prior to antireflux surgery. However, controversy exists regarding the value of traditional manometry to predict post-operative dysphagia after fundoplication. Today, high-resolution manometry (HRM) has replaced traditional water perfused systems for the analysis of esophageal physiology. The aim of this study was to evaluate the utility of HRM in predicting post-operative dysphagia in patients with an otherwise functioning Nissen fundoplication. METHODS Patients who underwent a laparoscopic Nissen fundoplication at a single institution were identified through a prospectively collected database. Patients were asked to undergo routine post-operative testing 6-12 months after surgery. Patients who had normal post-operative 24-hour pH test scores were eligible for the study. Of these patients, those without available raw data from preoperative HRM were excluded. Traditional ineffective motility (IEM) was defined as mean distal esophageal contraction amplitude of <30mmHg or 30% or less peristaltic waves. Post-operative dysphagia was graded using a standard scoring system (0= never, 1=1-2 times a month, 2=1-2 times per week, 3=daily). A symptom score of 2-3 was used to define post-operative dysphagia. Regression and association analysis of pre-operative manometric risk-factors were performed to determine predictors of post-operative dysphagia. P-values <0.05 were considered significant. RESULTS 95 patients (41 male; 54 female) were included in the analysis. Mean post-operative length of follow up was 14.9 months (range: 2-73). 70.2% patients had normal scores on all HRM parameters. Any dysphagia was reported by 50% of patients (17% grade-1, 23.4% grade-2, and 9.5% grade-3) Nineteen patients had traditional IEM. Of those with dysphagia, one also had traditional IEM. On univariate analysis only distal latency (DL) was found to be a significant predictor (p<0.001) of grade-3 but not grade-2 dysphagia. On multivariate analysis, no preoperative factors were found to be significant predictors of grade-3 dysphagia, but contraction front velocity predicted grade2 dysphagia. CONCLUSION Persistent daily dysphagia occurs in ~10% of patients following an otherwise successful Nissen fundoplication. Advancements in manometric technology provide additional data points in the preoperative analysis of these patients. This analysis reveals that elevated integrated relaxation pressure (IRP) is a useful new metric to predict post-operative dysphagia in addition to traditional identification of weak distal esophageal contraction amplitudes. Pre-operative factors as predictors of post-fundoplication dysphagia

Common Fixed Point Theorems for Weak Contraction Mapping of Integral Type in Modular Spaces

In this paper, we prove three common fixed point theorems for weak contraction map- pings of integral type in modular spaces. In the first theorem we prove a common fixed point of ρ−compatible mappings satisfying a (φ − Ψ)−weak contraction. The second theorem is another version of the first theorem. In the third theorem we study a common fixed point of ρ−compatible mappings in modular spaces involving altering distances of integral type. The results extended several similar results in metric and Banach spaces.

On the topology and wt-distance on metric type spaces

Abstract Recently, Khamsi and Hussain (Nonlinear Anal. 73:3123-3129, 2010) discussed a natural topology defined on any metric type space and noted that this topology enjoys most of the metric topology like properties. In this paper, we define topologically complete type metrizable space and prove that being of metrizability type is preserved under a countable Cartesian product and establish the fact that any G δ set in a complete metric type space is a topologically metrizable type space. Next, we introduce the concept of wt-distance on a metric type space and prove some fixed point theorems in a partially ordered metric type space with some weak contractions induced by the wt-distance. MSC:47H09, 47H10.

Concerted actions of TXA2 and mechanical stretch stimulate NOS3 (eNOS) in rat pulmonary arterial myocytes putatively via ROS generation and mechanosensitive channel activation (LB673)

Nitric oxide (NO), a potent vasodilator, is produced by type 3 NO synthase (NOS3, eNOS) in endothelium. In endothelium‐denuded pulmonary arteries (PAs) from rat, however, we found that unspecific NOS inhibitor (L‐NAME) induces a weak contraction in the presence of 2 ‐ 5 nM U46619 (thromboxane A2 agonist). With additional increase in wall tension equivalent to pressure elevation to 30 mmHg (pre‐stretch), L‐NAME induced robust contraction of PAs (L‐NAME contraction; 110 % of 80 mM KCl contraction). In endothelium‐denuded systemic arteries (e.g. renal and mesenteric arteries), no such L‐NAME induced contraction was observed. Interestingly, contraction of PAs by 20 mM KCl and 2 nM U46619 was also robustly augmented by L‐NAME, suggesting that the pre‐stretch effect was mimicked by partial depolarization. Pretreatment with 30 µM DIDS, known as an inhibitor of stretch‐activated cation channels (SACs) in arterial myocytes, the L‐NAME contraction was abolished in the PAs with pre‐stretch. The L‐NAME contraction was also diminished by ROS scavengers (Tiron and PEG‐Catalase). Consistently, exogenous hydrogen peroxide (H2O2, 1 µM) effectively augmented the contraction by L‐NAME without pre‐stretch whereas 1 µM H2O2 alone had no effect. Neither NOS1 inhibitor (SMTC) nor NOS2 inhibitor (1400W) mimicked the L‐NAME contraction. Muscular expression of NOS3 was confirmed by RT‐PCR and immunohistochemistry. Taken together, we suggest that PA myocytes express NOS3 that is concertedly activated by TXA2 and mechanical stretch. ROS generation and facilitated SACs by wall stretch might mediate the NOS3 recruitment in PA myocytes, and the resultant decrease in the contractility might contribute to the relatively low peripheral resistance of pulmonary circulation with fluctuating PA pressure.

Origin of weak layer contraction in de Vries smectic liquid crystals.

Structural investigations of the de Vries smectic-A (SmA) and smectic-C (SmC) phases of four mesogens containing a trisiloxane end segment reveal a linear molecular conformation in the SmA phase and a bent conformation resembling a hockey stick in the SmC phase. The siloxane and the hydrocarbon parts of the molecule tilt at different angles relative to the smectic layer normal and are oriented along different directions. For the compounds investigated, the shape of orientational distribution function (ODF) is found to be sugarloaf shaped and not the widely expected volcano like with positive orientational order parameters: ⟨P2⟩ = 0.53-0.78, ⟨P4⟩ = 0.14-0.45, and ⟨P6⟩∼0.10. The increase in the effective molecular length, and consequently in the smectic layer spacing caused by reduced fluctuations and the corresponding narrowing of the ODF, counteracts the effect of molecular tilt and significantly reduces the SmC layer contraction. Maximum tilt of the hydrocarbon part of the molecule lies between approximately 18° and 25° and between 6° and 12° for the siloxane part. The critical exponent of the tilt order parameter, β∼0.25, is in agreement with tricritical behavior at the SmA-SmC transition for two compounds and has lower value for first-order transition in the other compounds with finite enthalpy of transition.

On inclusion of F-contractions in ( δ , k ) -weak contractions

We obtain a certain property of F-contractions, which enables us to generalize and extend Wardowski’s (Fixed Point Theory and Applications 2012:94, 2012) result and other fixed point theorems to the class of nonexpansive operators in real Banach spaces. We give illustrative examples to demonstrate nontrivial applicability of the property and use it to prove that F-contractions are closely related to -weak contractions introduced by Berinde (Carpath. J. Math. 19(1):7-22, 2003; Nonlinear Anal. Forum 9(1):43-53, 2004). MSC:47H09, 47H10, 54H25.

A Novel Structural Unit in the N-terminal Region of Filamins

Immunoglobulin-like (Ig) domains are a widely expanded superfamily that act as interaction motifs or as structural spacers in multidomain proteins. Vertebrate filamins (FLNs), which are multifunctional actin-binding proteins, consist of 24 Ig domains. We have recently discovered that in the C-terminal rod 2 region of FLN, Ig domains interact with each other forming functional domain pairs, where the interaction with signaling and transmembrane proteins is mechanically regulated by weak actomyosin contraction forces. Here, we investigated if there are similar inter-domain interactions around domain 4 in the N-terminal rod 1 region of FLN. Protein crystal structures revealed a new type of domain organization between domains 3, 4, and 5. In this module, domains 4 and 5 interact rather tightly, whereas domain 3 has a partially flexible interface with domain 4. NMR peptide titration experiments showed that within the three-domain module, domain 4 is capable for interaction with a peptide derived from platelet glycoprotein Ib. Crystal structures of FLN domains 4 and 5 in complex with the peptide revealed a typical β sheet augmentation interaction observed for many FLN ligands. Domain 5 was found to stabilize domain 4, and this could provide a mechanism for the regulation of domain 4 interactions.

Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces. Keywords—Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

Case Scenario: Residual Curarization in Diabetic Polyneuropathy

Case Scenario: Residual Curarization in Diabetic Polyneuropathy

Rational Contractions in b-Metric Spaces

In this paper, we prove fixed point theorems for contractions and generalized weak contractions satisfying rational expressions in complete b-metric spaces. Our results generalize several well-known comparable results in the literature.

(ψ,φ)-weak contraction on ordered uniform spaces

In this paper, we prove a fixed point theorem for (?,?)-contractive mappings on ordered uniform space.