Mappings In Metric Spaces Research Articles

Fixed point theorem for generalized Chatterjea type mappings

We introduce a new type of mappings in metric spaces which arethree-point analogue of the well-known Chatterjea type mappings, and call themgeneralized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the case of Chatterjea type mappings and this new class includesthe class of Chatterjea type mappings. The fixed point theorem for generalizedChatterjea type mappings is proven.

Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces

Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces

Best proximity point results for generalized proximal $Z$-contraction mappings in metric spaces and some applications

In this paper, we define generalized proximal Z-contraction mappings of first and second kind in a metric space (X, d). The existence of best proximity point is shown for the defined mappings under some specific conditions which generalizes and extends some existing results of Olgun et al. [23] and Abbas et al. [1]. Suitable examples are given to justify the derived results. Some applications are also shown via fixed point formulation for such mappings in variational inequality problem and homotopy result.

Determination of the Fixed Point of Lotka-Volterra Function

The paper focuses on the Lotka-Volterra function in its discrete form. The purpose of the study was to determine the fixed points of the function. The study employs the Banach Fixed Point Theorem and Contraction Mapping in Metric Space on the function to demonstrate the uniqueness of the fixed points and its continuous stability after several iterations, using the fixed points as the initial conditions. The study has shown that $(0,0),\left(0,\frac{\alpha-1}{\beta}\right),\left(\frac{1+\gamma}{\delta},0\right)$ and $\left(\frac{1+\gamma}{\delta},\frac{\alpha-1}{\beta}\right) $are the fixed points of the function, with the initial pair serving as a trivial one and the other three solely depending on the parameter values for the behavior of the function. The outcome of the limit points of the function as the fixed points after several iterations forms a fixed orbit structure of the function, irrespective of the value of the parameter. The study also showed the uniqueness of the fixed points, demonstrating the stability and continuity of the function in its steady state.

On Reich and Chaterjea type cyclic weakly contraction mappings in metric spaces

On Reich and Chaterjea type cyclic weakly contraction mappings in metric spaces

New Fixed Point Theorems for θ − ω − Contraction on λ , μ -Generalized Metric Spaces

In this paper, we consider a new extension of the Banach contraction principle, which is called the θ − ω − contraction inspired by the concept of θ − contraction in λ , μ -generalized metric spaces and to study the existence and uniqueness of fixed point for the mappings in metric space. Moreover, we discuss some illustrative examples to highlight the improvements that were made, and we also give an iterated application of linear integral equations.

Common Best Proximity Points for Proximal Weak Commuting Mappings in Metric Spaces

Common Best Proximity Points for Proximal Weak Commuting Mappings in Metric Spaces

On $\theta$-convex contractive mappings with application to integral equations

The fundamental goal of our paper is to study $\theta$-convex contractive mappings in metric spaces. We demonstrate some fixed point results for such mappings. Also, we give an application to integral equations of our results. Consequently, our results encompass numerous generalizations of the Banach contraction principle on metric space.

Three Convergence Results for Iterates of Nonlinear Mappings in Metric Spaces with Graphs

In 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable under the presence of small errors. In the present paper, we obtain an extension of this result for self-mappings of a metric space with a graph.

Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for contraction mapping in metric spaces, have developed rapidly in recent years. Some of the things that support the development of generalization are the emergence of mappings that are more general than contraction mappings and the emergence of spaces that are more general than metric spaces. The generalized Kannan type mappings are one of the mappings that are more general than contraction mappings. Furthermore, some of the more general spaces than metric spaces are b-metric spaces and modular b-metric spaces, which bring the concept of b-metric spaces into modular spaces. The fixed-point theorems for generalized Kannan-type mappings on b-metric spaces have been given. Therefore, this research aims to define generalized Kannan-type mappings on modular b-metric spaces and provide fixed point theorems for the generalized Kannan-type mappings on complete modular b-metric spaces. The definition of generalized Kannan type mapping in modular b-metric spaces is given by generalizing generalized Kannan type mappings in b-metric spaces. Then, the proof of fixed-point theorems for that mapping in modular b-metric spaces is carried out analogously to the proof of the fixed-point theorems for that mapping given in b-metric space. In this article, we obtain the definition of Kannan-type mappings and fixed-point theorems for generalized Kannan-type mappings in modular b-metric spaces and some consequences of the fixed-point theorem. In proving the theorem, a property of altering distance functions in b-metric spaces is generalized into modular b-metric spaces.

Best Proximity Point Results for n-Cyclic and Regular-n-Noncyclic Fisher Quasi-Contractions in Metric Spaces

In this work, we introduce some new concepts such as n-cyclic Fisher quasi-contraction mappings, full-n-noncyclic and regular-n-noncyclic Fisher quasi-contraction mappings in metric spaces. We then generalize the results by Safari-Hafshejani, Amini-Harandi and Fakhar. Meanwhile, we answer the question “under what conditions does a full-n-noncyclic Fisher quasi-contraction mapping have n(n−1)/2 unique optimal pairs of fixed points?”. Further, to support the main results, we highlight all of the new concepts via non-trivial examples.

Around metric coincidence point theory

Let $(X,d)$ be a complete metric space, $(Y,\rho)$ be a metric space and $f,g:X\to Y$ be two mappings. The problem is to give metric conditions which imply that, $C(f,g):=\{x\in X\ |\ f(x)=g(x)\}\not=\emptyset$. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, \emph{Teoria punctului fix \^in analiza func\c tional\u a}, Babe\c s-Bolyai Univ., Cluj-Napoca, 1973), A. Buic\u a (A. Buic\u a, \emph{Principii de coinciden\c t\u a \c si aplica\c tii}, Presa Univ. Clujean\u a, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, \emph{Co\-vering mappings in metric spaces and fixed points}, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petru\c sel (A. Petru\c sel, \emph{A generalization of Peetre-Rus theorem}, Studia Univ. Babe\c s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.

Capacitary density and removable sets for Newton–Sobolev functions in metric spaces

In a complete metric space equipped with a doubling measure and supporting a (1, 1)-Poincaré inequality, we show that every set satisfying a suitable capacitary density condition is removable for Newton–Sobolev functions.

Best Proximity Points for Generalized Geraghty Quasi-Contraction Type Mappings in Metric Spaces

In this paper, we introduce a new concept of α-φ-Geraghty proximal quasi-contraction type mappings and establish best proximity point theorems for those mappings in proximal T-orbitally complete metric spaces. This generalizes and complements the proofs of some known fixed and best proximity point results.

Method of search functionals and its applications in fixed point and coincidence theory

The paper contains a survey of several results from the author’s papers and joint papers by the author and Yu. N. Zakharyan, both on the zero existence and approximation for single-valued and multivalued (α, β)-search functionals, and also on the zero existence preservation for parametric family of such functionals, under the parameter changing. Some corollaries of these results in the fixed point and coincidence theory of single-valued and multi-valued mappings of metric spaces are also given. The comparison is provided with some known results by other authors. In the concluding part of the paper, we investigate the problem on the existence of a parameter-continuous single-valued branch of zeros for a parametric family of search functionals. A theorem on the existence of solution of this problem is proved.

Fixed Points and Common Fixed Points for Orbit-Nonexpansive Mappings in Metric Spaces

In this paper, we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric spaces. The innovative concept studied here deals with nonexpansivity conditions with respect to orbits and under assumptions that only depend on the features of the closed balls of the metric space.

Fixed Point Theorems Using α-Admissible Mappings in Metric Spaces

In this paper, we shall prove the fixed point theorems in metric space using \(\alpha\) - admissible mapping. Some existing results of literature shall be deduced from the main results. In the end, we shall provide an example to support our result.

Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques

<abstract><p>In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and $ \Delta $-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasi-nonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in <xref ref-type="table" rid="Table1">Table 1</xref>. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces.</p> </abstract>

Fixed point theorem for a new SF-GF-contraction mappings in metric space with supportive applications

This manuscript has for goal to present a new type of contraction, namely SF -GF -contraction, based on the simulation function and the Geraghty function. Some existence and uniqueness results of fixed point in complete metric spaces have been shown with this contraction. Our results generalize and unify several existing results in the literature. Moreover, we illustrated these results with some examples and applications.

Existence results for single and multivalued mappings in metric spaces with applications

Existence results for single and multivalued mappings in metric spaces with applications