Weak Contraction Mappings Research Articles

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.

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.

Application on Atangana-Baleanu fractional derivative via (τ, a)-weak contractive mappings

Application on Atangana-Baleanu fractional derivative via (τ, a)-weak contractive mappings

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.

Fixed-point theorems of {F}^{star}- ( psi,phi ) integral-type contractive conditions on 1_{E}-complete multiplicative partial cone metric spaces over Banach algebras and applications

In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1_{E}-complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.

Weak Wardowski contractive multivalued mappings and solvability of generalized phi-Caputo fractional snap boundary inclusions

In this paper, we introduce the notion of weak Wardowski contractive multivalued mappings and investigate the solvability of generalized '-Caputo snap boundary fractional differential inclusions. Our results utilize some existing results regarding snap boundary fractional differential inclusions. An example is given to illustrate the applicability of our main results.

Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area.

Fixed Point Theorems for Integral-type Weak-Contraction Mappings in Modular Metric Spaces

Abstract In 2013, Azadifar et al. [3] established fixed point result in integral type contraction in modular metric space and 2020, Chaira et al.[11] established some extensions of Fixed Point Theorems for Weak-Contraction Mapping in Partially Ordered Modular Metric Spaces. In this paper we have established some common fixed point results in integral type contractions in modular and convex modular metric spaces.

On (α,φ)-weak Pata contractions

In this paper, we give (α,φ)-weak Pata contractive mapping by using the simulation function and multivalued (α,φ)-weak Pata contractions and establish some fixed point results for such contractions. Also, we give an example related to (α,φ)-weak Pata contractive mappings via simulation function. Our results generalize some Pata-type contractions and Banach contractions. Consequently, the obtained results encompass several results in the literature.

On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces

Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {\em J. Fixed Point Theory Appl.} {\bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_\lambda$, where $\lambda\in (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called double averaged mapping. The first attempt is to prove the existence and uniqueness of the fixed point of a double averaged mapping associated with a weak enriched contraction mapping. Based on this result on Banach spaces, we give some sufficient conditions for the equality of all fixed points of a double averaged mapping and the set {of all fixed points of a weak enriched contraction mapping.} Moreover, our results show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a weak enriched contraction mapping. An illustrative example for showing the efficiency of our results is given.

Common fixed point of Kannan and weak contractive type mappings on a modular metric space endowed with a graph

In this paper, we reformulate, extend, and establish certain fixed point findings for Kannan type contraction mappings in a modular metric space with a graph. This paper’s result is novel and adds to the previously published result of a graph-endowed metric, modular metric spaces.

Some fixed point results in ordered $b$-metric space with auxiliary functions

The purpose of this paper is to establish some fixed point results for a class of generalized $(\phi, \psi)$-weak contraction mapping in a partially ordered $b$-metric space. This mapping necessarily have a unique fixed point under ordered relation in a space. Also, the results for common and coincidence fixed points of the self mappings are presented. These results generalize and extend an existing results in the literature. Some illustrations are given at the end to support the results.

Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications

In this paper, we construct a new hybrid iteration, called SR-iteration, and prove its stability and convergence analysis for weak contraction mappings in a Banach space. We compare rate of convergence between the SR-iteration and other iterations. Moreover, we provide numerical comparisons for supporting our main theorem and apply our main result to prove existence problem of mixed type Volterra-Fredholm functional nonlinear integral equation.

Existence of best proximity points satisfying two constraint inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

$${S}_{H}$$-metric spaces and fixed-point theorems for multi-valued weak contraction mappings

$${S}_{H}$$-metric spaces and fixed-point theorems for multi-valued weak contraction mappings

Remarks of Fixed Point for (ψ,φ)-Weakly Contractive Mappings

In this paper, we obtain a new fixed point theorem for weak contraction mappings on complete generalized metric spaces. Our result is different from that of (ψ,φ)-weakly contractive mappings which had been obtained by Lakzian–Samet’s [Appl. Math. Lett. 25 (2012) 902–906]. Moreover, an example is given to illustrate the usability of the obtained result.

Common fixed point of Kannan and weak contractive type mappings on a modular metric space endowed with a graph

Common fixed point of Kannan and weak contractive type mappings on a modular metric space endowed with a graph