Fixed Point Results Research Articles

Some Relation-Theoretic Fixed Point Results in Fuzzy Metric Spaces

Some Relation-Theoretic Fixed Point Results in Fuzzy Metric Spaces

New fixed point results of some enriched contractions in CAT(0) spaces

New fixed point results of some enriched contractions in CAT(0) spaces

G-metric spaces and the related approximate fixed point results

G-metric spaces and the related approximate fixed point results

Fixed point theorems for generalized contractions in $ \mathfrak{F} $-bipolar metric spaces with applications

<abstract><p>The major objectives of this research article are to introduce the notion of ($ \alpha, \psi $)-contraction in the context of $ \mathfrak{F} $-bipolar metric space and establish fixed point theorems. In this way, coupled fixed point results are obtained by applying the leading theorems. Some non-trivial examples are also furnished to show the validity of established results. As applications of the main result, we investigate the solution of an integral equation and a homotopy problem.</p></abstract>

Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations

<abstract><p>In this manuscript, the concept of rational-type multivalued $ F- $contraction mappings is investigated. In addition, some nice fixed point results are obtained using this concept in the setting of $ MM- $spaces and ordered $ MM- $spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application.</p></abstract>

Some new results in $ \mathcal{F} $-metric spaces with applications

<abstract><p>In this research article, we give the notion of graphic $ F $-contraction in the setting of $ \mathcal{F} $-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally $ G $ -continuous graphic $ F $-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.</p></abstract>

FIXED POINT RESULTS FOR MULTI-VALUED GRAPH CONTRACTIONS ON A SET ENDOWED WITH TWO METRICS

In this paper we will study existence, uniqueness and data depen­dence of the fixed points of multi-valued operators on a set endowed with two metrics. The case of multi-valued graph contractions is con­sidered. Then, an extension to a more general contraction type condi­tion is also given.

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results

Krasnoselskii-type results for equiexpansive and equicontractive operators with application in radiative transfer equations

<abstract><p>In this paper, we study the results of fixed points for the operator equations of type $ x = H(\digamma x, x) $ using the idea of measure of noncompactness and assuming that the operator $ \digamma $ is $ k $ -set contractive (strictly $ k $ -set contractive, or a continuous) and the family $ \{H(u, .):u\} $ is equiexpansive or equicontractive. The obtained results are generalization of Krasnoselskii type fixed point results. Some examples are given to elaborate new concepts. We use the main result to find the existence of solutions for the stationary radiative transfer equation in a channel. We demonstrate our theory with an example by comparison of an approximate solution with the exact solution.</p></abstract>

NEW FIXED POINT RESULTS FOR GERAGHTY CONTRACTIONS AND THEIR APPLICATIONS

In this paper, we prove existence and uniqueness of fixed point involving Geraghty contraction in a metric space endowed with a binary relation. Moreover, we give an application to periodic boundary value problems regarding to ordinary differential equations (ODE).

Controllability and Observability Analysis of a Fractional-Order Neutral Pantograph System

In the recent past, a number of research articles have explored the stability, existence, and uniqueness of the solutions and controllability of dynamical systems with a fractional order (FO). Nevertheless, aside from the controllability and other dynamical aspects, very little attention has been given to the observability of FO dynamical systems. This paper formulates a novel type of FO delay system of the Pantograph type in the Caputo sense and explores its controllability and observability results. This research endeavor begins with the conversion of the proposed dynamical system into a fixed-point problem by utilizing Laplace transforms, the convolution of Laplace functions, and the Mittag–Leffler function (MLF). We then set out Gramian matrices for both the controllability and observability of the linear parts of our proposed dynamical system and prove that both the Gramian matrices are invertible, thus confirming the controllability and observability in a given domain. Considering the controllability and observability results of the linear part along with some other assumptions, we investigate the controllability and observability results related to the nonlinear system. The Banach contraction result, the fixed-point result of Schaefer, the MLF, and the Caputo FO derivative are used as the main tools for establishing these results. To establish the authenticity of the established results, we add two examples at the end of the manuscript.

Non-unique Fixed Points of Self Mappings in Bi-metric Spaces

In this paper, we prove a few non-unique fixed-point results of mapping on a set with bi-metrics using θ – contraction. We also give an example that justifies our results. In the literature, our result generalized many results

Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

<abstract><p>The goal of this paper is to present a new class of contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.</p></abstract>

Partially nonexpansive mappings

It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.

Fixed Points for (ξ,ω)-Weakly Cyclic Type Generalized Contraction Condition in Metric Spaces with an Application

In the present work, we have introduced a new type of (ξ,ω)-weakly cyclic generalized contraction in the setting of metric spaces and established some fixed-point results. Fixed-point results are useful in establishing the existence of unique solution to differential equations. We have supplemented the derived results with suitable non-trivial examples with an application to the Boundary Value Problem, generalizing some known results. The analytical result has been verified with numerical simulation.

Iterative Numerical Methods for a Fredholm–Hammerstein Integral Equation with Modified Argument

Iterative processes are a powerful tool for providing numerical methods for integral equations of the second kind. Integral equations with symmetric kernels are extensively used to model problems, e.g., optimization, electronic and optic problems. We analyze iterative methods for Fredholm–Hammerstein integral equations with modified argument. The approximation consists of two parts, a fixed point result and a quadrature formula. We derive a method that uses a Picard iterative process and the trapezium numerical integration formula, for which we prove convergence and give error estimates. Numerical experiments show the applicability of the method and the agreement with the theoretical results.

Coupled fixed point theorems of JS-G-contraction on G-metric spaces

Jaradat has proven some fixed point results using JS-G-contraction on $G-$metric spaces. Choudhury et al. were derived coupled fixed point theorems for the $G-$metric spaces. The purpose of this paper is to prove some coupled fixed point theorems of JS-G-contraction on G-metric spaces. Moreover, some example is presented to illustrate the validity of our results.

Symmetrical Hybrid Coupled Fuzzy Fixed-Point Results on Closed Ball in Fuzzy Metric Space with Applications

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying a new advanced contraction on a closed ball in the setting of complete fuzzy metric spaces. In addition, the new notion of hybrid fuzzy-graph-dominated mappings introduced in fuzzy metric spaces achieves some new advanced fuzzy fixed-point problems. Some new definitions and illustrative examples are given to validate our new findings. Lastly, to demonstrate the originality of our new results, we present an application to the Fredholm-type integral equation.

Fixed point theorems and periodic problems for nonlinear Hill’s equation

Two main results of fixed point theory in infinite dimensional space are Schauder’s theorem and the contraction mapping principle. Krasnoselskii combined them into one fixed point result. In this paper, we continue the study of extensions of these theorems investigating a convex modular in a original vector space, not in modular space and without Delta _{2} condition, to provide certain extensions of Banach contraction principle and Krasnoselskii fixed point theorem. We applied that theorem to solve the nonlinear periodic problem of Hill’s equation.

Almost automorphic solutions of second-order equations involving time scales with boundary conditions

In this article, we investigate the existence and uniqueness of solutions of linear and semilinear second–order equations involving time scales. To obtain such results, we make use of exponential dichotomy and fixed point results. Also, we present some examples and applications to illustrate our main results.