Contractions In Metric Spaces Research Articles

Fixed Point Theorems for Set-Valued Contractions in Metric Spaces

Fixed Point Theorems for Set-Valued Contractions in Metric Spaces

Rational Contraction in Metric Space and Common Fixed Point Theorems

The study of contraction mappings in fixed-point theory is a fascinating and crucial field of mathematics. The concept of contraction plays a vital role in proving the existence and uniqueness of fixed points. Banach's contraction theory offers a fixed point theorem that is widely accepted as unique in most analyses. By using rational expressions in metric spaces, we can achieve unique results in general contraction mapping. These results are based on several innovative ideas stemming from the latest research. The delivered results upgrade and federate many existing outcomes on the topic in the literature Bhardwaj, R. et al. (2007) Chouhan et al. (2014) and Garg and Priyanka (2016). Also gives some suitable examples for verifying our results.

Expansive Type Rational Contraction in Metric Space and Common Fixed Point Theorems

The field of expansive mappings in fixed-point theory is one of the most fascinating  areas in mathematics. In this theory, contraction is one of the main tools used to prove a fixed point's existence and uniqueness. For all of the analyses, the fixed point theorem proposed by Banach's contraction theory is highly popular and widely used to prove that a solution to the operator equation Tx=x exists and is unique. Through the present article, we utilize rational expressions in metric spaces to deliver unique common stable (fixed) point results in expansive mapping. The main outcomes of numerous relevant innovations in the newest research are built upon them.

General New Results on (ϕ,F)−Contractions in b−Metric-like-Spaces

Thispaper recognizes a general approach related to recent fixed point results about the classes of interpolative and hybrid contractions in metric space and general metric spaces. Considering auxiliary functions, so called Wardowski functions, and a rich set of implicit relations, we introduce types of (αvq,ϕ,F)−contractions and r−order hybrid (αvq,ϕ,F)−contractions in the setting of b−metric-like spaces. They generate and simplify many forms of contractions widely used in the literature. The resulting theorems significantly extend, generalize, and unify an excellent work on fixed point theory.

Fixed Point Results of a New Family of Contractions in Metric Space Endowed with a Graph

In this note, a general class of contractive inequality, namely, admissible hybrid H − α − ϕ contraction, is proposed in metric space endowed with a graph, and new criteria for which the mapping is a Picard operator are examined. The significance of this type of contraction is connected with the possibility that its inequality can be particularized in more than one way, depending on the provided constants. Relevant examples are designed to support the assumptions of our obtained notions and to show how they are different from the known ones. A corollary which reduces our obtained result to a recently published result in the literature is pointed out and discussed.

Fixed point results for $P$-contractions via $w$-distance

"In the present paper, we define the $Pw$-contraction by considering the inequality called $P$-contraction in metric space together with the $w$ -distance. We then present fixed point theorems for both single-valued and multivalued $Pw$-contractions. We also support our results with suitable examples."

Some new φ-fixed point and φ-fixed disc results via auxiliary functions

In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for (gamma ,psi ,varphi ,phi ) contractions, rational-(gamma , psi ,varphi ,phi ) contractions and almost-(gamma ,psi , varphi ,phi ) contractions and φ-fixed disc results for (psi ,varphi ,phi )_{x_{0}} type 1 contractions, (psi ,varphi ,phi )_{x_{0}} type 2 contractions, and (psi ,varphi ,phi )_{x_{0}} type 3 contractions in metric spaces. We generalize some existing φ-fixed point and φ-fixed circle results in the literature. Further, we give some examples to demonstrate the usefulness of our results and investigate the existence and uniqueness of solutions of nonlinear integral equations.

A fixed point principle in ordered metric spaces and applications to rational type contractions

<abstract><p>Fixed points results for rational type contractions in metric spaces have been widely studied in the literature. In the last years, many of these results are obtained in the context of partially ordered metric spaces. In this paper, we introduce a fixed point principle for a class of mappings between partially ordered metric spaces that we call orbitally order continuous. We show that the hypotheses in the statement of such a principle are not redundant and, in addition, that they cannot be weakened in order to guarantee the existence of a fixed point. Moreover, the relationship between this kind of mappings and those that are continuous and orbitally continuous is discussed. As an application, we extend many fixed point theorems for continuous contractions of rational type to the framework of those that are only orbitally order continuous. Furthermore, we get extensions of the aforementioned metric fixed point results to the framework of partial metrics. This is achieved thanks to the fact that each partial metric induces in a natural way a metric in such a way that our new principle is applicable. In both approaches, the metric and the partial metric, we show that there are orbitally order continuous mappings that satisfy all assumptions in our new fixed point principle but that they are not contractions of rational type. The explored theory is illustrated by means of appropriate examples.</p></abstract>

Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.

Convergence of inexact iterates of strict contractions in metric spaces with graphs

Convergence of inexact iterates of strict contractions in metric spaces with graphs

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.

Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

New fixed point results for Proinov–Suzuki type contractions in metric spaces

New fixed point results for Proinov–Suzuki type contractions in metric spaces

A fixed point theorem for (\phi, \shi)-convex contraction in metric spaces

In the present paper, we introduce the notion of (\phi, \shi)-convex contraction mapping of order m and establish a fixed point theorem for such mappings in complete metric spaces. The present result extends and generalizes the well known result of Dutta and Choudhary (Fixed Point Theory Appl. 2008 (2008), Art. ID 406368), Rhoades (Nonlinear Anal., 47(2001), 2683-2693), Istratescu (Ann. Mat. Pura Appl., 130(1982), 89-104) and besides many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results.

Fixed point of set-valued graph contractions in metric spaces

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)subseteq Xtimes X.$

Coincidence best proximity point theorems for proximal Berinde g-cyclic contractions in metric spaces

In this paper, we introduce the notions of proximal Berinde g-cyclic contractions of two non-self-mappings and proximal Berinde g-contractions, called proximal Berinde g-cyclic contraction of the first and second kind. Coincidence best proximity point theorems for these types of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our main results extend and generalize many existing results in the literature.

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.

A new generalization of $\alpha$-type almost-$F$-contractions and $\alpha$-type $F$-Suzuki contractions in metric spaces and their fixed point theorems

In this paper a new generalization of $\alpha$-type almost-$F$-contractions and an extension of $\alpha$-type $F$-Suzuki contractions are given. Moreover, some new fixed point theorems of them are discussed. Some examples and applications in order to illustrate the main results are presented. The results of this article can be considered as improvements of some well-known results appeared in the literature.

Existence Results for Systems of Quasi-Variational Relations

We study the existence of solutions for a  system of variational relations, in a general form, using a fixed point result for contractions in metric spaces. As a particular case, we give sufficient conditions for the existence of solutions of a system of quasi-equilibrium problems. 

Fixed point results for nonlinear contractions with application to integral equations

We present a number of fixed and common fixed point theorems for a class of nonlinear contractions in metric spaces and metric spaces endowed with graphs. Our results complement, extend and generalize a number of fixed point theorems including a recent fixed point theorem of Kim et al. [Suzuki-type of common fixed theorem in metric spaces, J. Nonlinear Convex Anal. 16 (2015) 1779–1786]. We also discuss an application to a system of integral equations.