Weak Contractive Condition Research Articles

A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered s -Distance Spaces with an Application

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s -distance spaces under θ , ϕ , ψ -type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

Fixed points for intimate mappings

In this paper, we introduce (ψ,φ)-weak contraction condition that involves cubic terms of distance function. We prove some fixed point theorems for pairs of intimate mappings satisfying newly introduced contraction condition and generalize the result of Murthy and Prasad [14] and Jain et al. [8]. At the end, an application for integral type contraction condition is given.

Weak contraction condition for faintly compatible mappings involving cubic terms of metric functions

In this paper, we obtain a generalized common fixed point theorem for four mappings using the conditions of non-compatibility and faint compatibility satisfying a generalized ∅−weak contraction condition that involves cubic terms of 𝑑(𝑥, 𝑦). Also, we provide an example in support of our result.

Osobina P u modularnim metričkim prostorima

Introduction/purpose: The aim of this paper is to present the concept of the generalized ∅-weak contractive condition involving various combinations of d(x,y) in modular metric spaces. Methods: Conventional theoretical methods of functional analysis. Results: This study presents the result of (Murthy & Vara Prasad, 2013) for a single-valued mapping satisfying a generalized ∅ -weak contractive condition involving various combinations of d(x,y). It is generalized in the setting of modular metric spaces, and then it is proved that this single-valued map satisfies the property P. In the end, an example is given in support of the result. Conclusion: With proper generalisations, it is possible to formulate well-known results of classical metric spaces to the case of modular metric spaces.

Common fixed points for generalized ψ-∅-weak contraction in metric space

In this paper, we first prove some common fixed point theorems for weakly compatible mappings, Point wise and R-weakly commuting mappings, Reciprocally continuous Mappings, R-weakly commuting mappings of type (Af), type (Ag), type (P) satisfying a generalized ∅-weak contraction condition that involves cubic terms of . Secondly, we prove common fixed point theorems for weakly compatible mappings along with (E.A) property and (CLR) property. At the last of each theorems, we give corollaries and applications in support of our theorems.

Set-valued Contractions in b-Metric Spaces with Application

In this article, we present a (α, F)-set-valued mapping in setting b-metric space by characterizing the weak contraction condition with the C function and the α-set-valued function of type S. There are examples and implementations accessible that illustrate the validity of our findings.

Notes on Krasnoselskii-type fixed-point theorems and their application to fractional hybrid differential problems

In this paper we prove a new version of Kransoselskii's fixed-point theorem under a ($\psi, \theta, \varphi$)-weak contraction condition. The theoretical result is applied to prove the existence of a solution of the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators orders of $0<\alpha<1$ and $\beta>0:$ \begin{equation}\nonumber \left\{\begin{array}{ll} D^{\alpha}[x(t)-f(t, x(t))]=g(t, x(t), I^{\beta}(x(t))), \,\,\, \text{a.e.} \,\,\, t\in J,\,\, \beta>0,\\ x(t_{0})=x_{0}, \end{array} \right. \end{equation} where $D^{\alpha}$ is the Riemann-Liouville fractional derivative order of $\alpha,$ $I^{\beta}$ is Riemann-Liouville fractional integral operator order of $\beta>0,$ $J=[t_{0}, t_{0}+a],$ for some fixed $t_{0}\in \mathbb{R},$ $a>0$ and the functions $f:J\times \mathbb{R}\rightarrow \mathbb{R}$ and $g:J\times \mathbb{R}\times \mathbb{R}\rightarrow \mathbb{R}$ satisfy certain conditions. An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

Common fixed points for generalized ψ-∅-weak contraction in metric space

In this paper, we first prove some common fixed point theorems for weakly compatible mappings, Point wise and R-weakly commuting mappings, Reciprocally continuous Mappings, R-weakly commuting mappings of type (Af), type (Ag), type (P) satisfying a generalized ∅-weak contraction condition that involves cubic terms of . Secondly, we prove common fixed point theorems for weakly compatible mappings along with (E.A) property and (CLR) property. At the last of each theorems, we give corollaries and applications in support of our theorems.

Fuzzy generalized weak contraction and its application to Fredholm non-linear integral equation in fuzzy metric space

The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of self maps in a fuzzy metric space,which is in accordance with the theory of metric spaces given by Rhoades (Nonlinear Analysis 47:2683–2693, 2001). Our results generalize existing fuzzy contraction (by Gregori and Sapena (Fuzzy Sets System 125:245–252, 2002), which is for only one self map. Using this, we establish a unique common fixed point theorem for two self-maps through weak compatibility. The article includes an example, in support of our results. Also an application we established, for the existence and uniqueness of a solution of Fredholm non-linear integral equation in the setting of fuzzy metric space.

Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras

In this work, we define the concept of a generalized c-distance in cone b-metric spaces over a Banach algebra and introduce some its properties. Then, we prove the existence and uniqueness of fixed points for mappings satisfying weak contractive conditions such as Han–Xu-type contraction and Cho-type contraction with respect to this distance. Our assertions are useful, since we remove the continuity condition of the mapping and the normality condition for the cone. Several examples are given to support the main results.

Compatible mappings and its variants for generalized ψ-∅-weak contraction condition

In the present paper, first we introduce generalized ψ-∅-weak contraction condition that involves cubic and quadratic terms of distance function d(x,y) and then proved common fixed point theorems for compatible mappings. Secondly, we deal with variants of compatible mappings type (K), type (R) and type (E). At the end, we provide applications of our results.

Hyperbolic spaces and directional contractions

The axiomatic approach to metric convexity goes back to the pioneering work of Karl Menger in 1928. This is an overview of this concept and the role it plays in metric fixed point theory especially in conjunction with spaces possessing a “hyperbolic” type structures. These include the CAT(0) spaces, hyperconvex metric spaces, and [Formula: see text]-trees. Much of the discussion involves the existence of “approximate” fixed point sequences for mappings satisfying weak contractive conditions. Applications of a well-known fixed point theorem due to Caristi are also included. These involve fixed and approximate fixed points for mappings satisfying local “directional” contractive and non-expansive conditions. Convexity plays a role in this part of the discussion as well. While the paper is semi-expository in nature, some detailed proofs appear here for the first time. Also the concept of a weak [Formula: see text]-directional contraction introduced in Sec. 8 appears to be new. Several suggestions for further research are also discussed.

Iterated Function Systems with the Weak Average Contraction Conditions

This paper concerns the chaos game of random iterated function systems. We consider a random iterated function system IFS() generated by a finite family of Lipschitz maps on a compact ball of ℝn with the weak average contraction condition and show that it admits a quasi-attractor satisfying the deterministic chaos game. In particular, these properties are preserved under small perturbations of the iterated function system IFS() with respect to the Lipschitz topology.

Fixed point of ($$\psi ,\phi$$) contractions on metric spaces

The aim of this paper is to obtain a fixed point theorem for mappings satisfying a generalized (\(\psi , \phi\))-weak contractive type condition in a complete metric space. Moreover, our result also generalizes some well known theorems in the literature.

Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application

In this paper, by characterizing a weak contractive condition based on using C − functions and α − admissible multi-valued mapping of type S, we present some fixed point results for ( α , F ) − admissible multi-valued mappings in the setting of b − metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is to take new contraction self-mappings in b − metric spaces for multi-valued mappings.

Common fixed point theorems for weak contractive conditions in metric spaces

Common fixed point theorems for weak contractive conditions in metric spaces

Notes on multidimensional fixed-point theorems

Abstract In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

The Existence of ϒ-fixed Point for the Multidimensional Nonlinear Mappings Satisfying (ψ,θ,φ)-weak Contractive Conditions

In this paper we prove the existence of ϒ-fixed point for a multidimensional nonlinear mappings F : Xk → X defined on the partially ordered metric spaces and satisfying (ψ, θ, ϕ)-weak contractive conditions. Moreover, we prove the uniqueness of that fixed point under extra conditions to (ψ, θ, ϕ)-weak contractive conditions.

Fixed point results for generalized [formula omitted]-weak contractions with an application to system of non-linear integral equations

The aim of this paper is to prove fixed point results under (ψ,ϕ)-weak contractive condition for continuous weak compatible mappings in ordered b-metric spaces. The results proved herein generalize, modify and unify some recent results of the existing literature. An application demonstrating the usability of our established results is also discussed besides furnishing an illustrative example.

Some common fixed point theorems for tangential generalized weak contractions in metric-like spaces

In this paper we define the tangential property in partial metric spaces to prove a common fixed point theorems for two pairs of self mappings, which satisfying a generalized weak contractive condition as well as satisfying a generalized contraction, an example is given to illustrate ours results.