Point Theorems For Contractive Mappings Research Articles

Common Fixed Point Theorems for Contractive Mappings of Integral Type in $$b$$-Metric Spaces

Common Fixed Point Theorems for Contractive Mappings of Integral Type in $$b$$-Metric Spaces

Fixed point theorems of contractive mappings on soft parametric metric space

<abstract><p>The purpose of this study was to introduce soft topology generated by soft parametric metric space and prove Banach's fixed point theorem as an extension of soft complete parametric metric space. An illustrative example was given by using this fixed point theorem.</p></abstract>

Fixed Point Result on Generalized Cone b-Metric Spaces

The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George <i>et al</i>. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.

Some Fixed Point Theorems of Contractive Mappings in P b r -Cone Metric Spaces over Banach Algebras

In this paper, we introduce the concept of a P b r -cone metric space over Banach algebras and prove some fixed point results under various contractive mappings in such a space. Some examples are given to elucidate the results. Our results extend and generalize many existing results in the literature.

A GENERALIZATION OF AN EXTENDED b-METRIC SPACE AND SOME FIXED POINT THEOREMS

In this paper, we present fixed point theorems for contraction mappings in a generalization of an extended $b$-metric space where the product of the Lipschitz constant and functions of the underlying space in the limit are bounded by one for sequences in an orbit. Futhermore, we prove fixed point results in which the contraction involves $b$-comparison functions.

Fixed Point Theorems for Contractive Mappings in Probabilistic Modular Spaces

In this paper we introduce the concept of contractive maps and prove some related fixed point theorems in probabilistic modular spaces. In addition, we investigate the existence of common fixed points for a finite linear combination of contractive mappings. Finally, some results concerned with the convergence properties of sequences defined by contractive maps in probabilistic modular spaces are also given.

Existence of fixed point theorems of contractive mappings in complete generalized metric spaces

Existence of fixed point theorems of contractive mappings in complete generalized metric spaces

A Revisit to n-Normed Spaces Through Its Quotient Spaces

In this paper, we define several types of continuous mapping in $n$-normed spaces with respect to the norms of its quotient spaces. Then, we show that all types of the continuity are equivalent. We also study contractive mappings on $n$-normed spaces using these norms. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in the $n$-normed space with respect to the norms of its quotient spaces.In the last section we prove a fixed point theorem and give some remarks on the $p$-summable sequence space as an $n$-normed space.

Fixed Point Theorems for Mizoguchi-Takahashi Type Contraction in Bicomplex-Valued Metric Spaces and Applications

The main aim of this paper is to study and establish some new fixed point theorems for contractive maps that satisfied Mizoguchi-Takahashi’s condition in the setting of bicomplex-valued metric spaces. These new results improve and generalize the Banach contraction principle and some well-known results in the literature. Finally, as applications of our results, we give the existence and uniqueness of the solution of a nonlinear integral equation.

Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel

Using some fixed point theorems for contractive mappings, including α-γ-Geraghty type contraction, α-type F-contraction, and some other contractions in mathcal{F}-metric space, this research intends to investigate the existence of solutions for some Atangana–Baleanu fractional differential equations in the Caputo sense.

SOME FIXED POINT THEOREMS FOR CONTRACTIVE MAPPINGS ON ORDERED ORTHOGONAL CONE METRIC SPACES

Very recently, orthogonal cone metric spaces, orthogonal completeness and orthogonal continuity are described in \cite{BG2019MS}. Also some fixed point theorems and their conclusions are proved on orthogonal cone metric spaces in there. In this paper, some fixed point theorems for contractive mappings are presented on ordered orthogonal cone metric spaces. Also an illustrative example is given.

Approximating Solutions of Non Linear First Order Abstract Measure Differential Equations by Using Dhage Iteration Method

In this paper we have proved the approximating solutions of the nonlinear first order abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability of given results in the paper. Sharma [2] initiated the study of nonlinear abstract differential equations and some basic results concerning the existence of solutions for such equations. Later, such equations were studied by various authors for different aspects of the solutions under continuous and discontinuous nonlinearities. The study of fixed point theorem for contraction mappings in partial ordered metric space is initiated by different authors. The study of hybrid fixed point theorem in partially ordered metric space is initiated by Dhage with applications to nonlinear differential and integral equations. The iteration method is also embodied in hybrid fixed point theorem in partially ordered spaces by Dhage [12]. The Dhage iteration method is a powerful tool for proving the existence and approximating results for nonlinear measure differential equations. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. In this paper we adopted this iteration method technique for abstract measure differential equations.

Common coupled fixed point theorems for two pairs of weakly compatible mappings in Menger metric spaces

Abstract In this paper, we prove some common coupled fixed point theorems for contractive mappings in Menger metric spaces under geometrically convergent t-norms. Also, we prove common fixed point theorems for pairs of weakly compatible mappings, which generalize the results of Jian-Zhong Xiao and al (2011). The main results is supported by a suitable examples.

Best proximity point theorems in topological spaces

Let A, B be nonempty subsets of a metric space X and $$f:A\rightarrow B$$ be a mapping. A point $$x_0\in A$$ is a best proximity point of f if $$d(x,f(x))=\mathrm{dist}(A,B):=\{d(a,b):a\in A,b\in B\}$$. It is worth mentioning that the metric function d plays a vital role in defining the notion of best proximity points. In this manuscript, we introduced a notion of best proximity points in arbitrary topological spaces and established few best proximity point theorems. Our main result generalizes the well-known Edelstein’s fixed point theorem for contractive mappings.

Ordered S_{p}-metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems

In this paper, we introduce the structure of S_{p}-metric spaces as a generalization of both S-metric and S_{b}-metric spaces. Also, we present the notions of S̃-contractive mappings in the setup of ordered S_{p}-metric spaces and investigate the existence of a fixed point for such mappings under various contractive conditions. We provide examples to illustrate the results presented herein. An application to periodic boundary value problems is presented.

New Fixed Point Results in Generalized Banach Space

In this paper, we prove some fixed point results dealing with rational type contractions on generalized Banach Space. Our results in the new cotext extend and completement fixed point theorems of contractive mappings. Also we present certain common point result for such contraction.

Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings

In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results.

An application of Perov type results in gauge spaces

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s sense on spaces endowed with a family of vector valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector valued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations.

Coincidence Theorems in New Generalized Metric Spaces Under Locally g-transitive Binary Relation

&lt;p&gt;In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].&lt;/p&gt;

Best proximity point theorems for contractive mappings

This article is concerned with some new best proximity point theorems for principal cyclic contractive mappings, proximal cyclic contractive mappings, and proximal contractive mappings. As a consequence, an interesting fixed point theorem, due to Edelstein, for a contractive mapping is obtained from all those best proximity point theorems.