Fixed Point Results Research Articles

Some Fixed-Point Theorems in Proximity Spaces with Applications

Considering the ω-distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.

Fixed Point of (α,β)-Admissible Generalized Geraghty F-Contraction with Application

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

Fixed Point Results for Generalized F-Contractions in b-Metric-like Spaces

The purpose of this paper is to introduce several generalized F-contractions in b-metric-like spaces and establish some fixed point theorems for such contractions. Moreover, some nontrivial examples are given to illustrate the superiority of our results. In addition, as an application, we find the existence and uniqueness of a solution to a class of integral equations in the context of b-metric-like spaces.

Fixed-Point Results Related to b-Intuitionistic Fuzzy Metric Space

In this study, we contribute to the terminological debate about various fixed-point results’ use of the term intuitionistic fuzzy b-metric space in defining the structure based on fuzzy sets. As a predominant result, we give an adequate condition for a sequence to be Cauchy in the intuitionistic fuzzy b-metric space. Subsequently, we simplify the proofs of manifold fixed-point theorems in the intuitionistic fuzzy b-metric spaces under the prominent contraction conditions. Also, we give a satisfactory condition for a solution to Cauchy in the intuitionistic fuzzy b-metric spaces.

Fixed point results of almost generalized $$(\phi , \psi ,\theta )_s$$-contractive mappings in ordered b-metric spaces

Fixed point results of almost generalized $$(\phi , \psi ,\theta )_s$$-contractive mappings in ordered b-metric spaces

Quadruple Best Proximity Points with Applications to Functional and Integral Equations

This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.

Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results

In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type space. We introduce a new metric space and prove analogs of Banach-, Kannan- and Reich-type fixed-point theorems. We also furnish various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in the literature.

Some fixed point results using F-weak expansive mapping in relation theoretic metric space

In this paper, we put forward the notion of F-weak expansive mapping and simultaneously prove some fixed point result specifically in relation theoretic metric space. In addition, our result generalizes one of the results obtained by [Jaroslaw Górnicki (2016). Fixed point theorems for F-expanding mappings, Fixed Point Theory and Applications, 2017(1)]. Also, some illustration is provided which further substantiates the result proved herein.

Fuzzy Fixed Point Results in Convex C ∗ -Algebra-Valued Metric Spaces

The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C ∗ -algebra-valued fuzzy λ -contraction and related concepts in a convex C ∗ -algebra-valued metric space ( C ∗ -AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approximate quantities is proposed. Consequently, two fixed point results of a C ∗ -algebra-valued fuzzy mapping ( C ∗ -AVFM) for the new type of contractions are established using Mann and Ishikawa iterative schemes. For some future investigations of our results, two open problems are noted concerning sufficient criteria guaranteeing the existence of fixed points of a C ∗ -algebra-valued fuzzy λ -contraction and whether or not the Picard iteration for a C ∗ -algebra-valued fuzzy λ -contraction converges.

On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein.

Fixed Point Results for a New Rational Contraction in Double Controlled Metric-like Spaces

In this paper, we present a new type of rational contraction in double controlled metric-like spaces and improve recent results of such spaces. Moreover, there is an example to verify the correctness of our results. Finally, we also obtain some new fixed point results, which can be derive directly from our main theorem.

Contraction Mappings in Intuitionistic Fuzzy Rectangular Extended B-Metric Spaces

In this study, we present the notion of intuitionistic fuzzy rectangular extended b-metric spaces as a generalization of intuitionistic fuzzy metric spaces and intuitionistic fuzzy rectangular b-metric spaces. Some well-known fixed-point results in metric fixed-point theory are generalized in the sense of intuitionistic fuzzy rectangular extended b-metric spaces. Several nontrivial examples and an application to nonlinear fractional differential equations are also imparted in this work to examine the validity of given results.

On Some w − Interpolative Contractions of Suzuki-Type Mappings in Quasi-Partial b-Metric Space

In this paper, our focus is to acquaint with the Suzuki-type mappings to establish some fixed point results using the new w-interpolative approach. We present some results for interpolative contraction operators via the w-admissible maps which satisfy the Kannan, Ćirić–Reich–Rus, and Hardy–Rogers contractions in quasi-partial b-metric space. Further, the outcomes so obtained are affirmed with relevant examples.

Common Attractive Point Results for Two Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces

In this work, we study some basic properties of the set of common attractive points and prove strong convergence results for common attractive points of two generalized nonexpansive mappings in a uniformly convex Banach space. As a consequence, we obtain a common fixed point result of such mappings and apply it to solving the convex minimization problem. Finally, numerical experiments are given to support our results.

Applications of some new Krasnoselskii-type fixed-point results for generalized expansive and equiexpansive mappings

We consider Ω as a subset of a Banach space W and Λ as a function of Ω into W. Let Ϝ be a function whose image values lie in W and domain is Lambda (Omega )times Omega or Omega times Omega . In this paper, we establish some fixed-point results for a generalized expansive and equiexpansive operator Ϝ such that Omega subseteq digamma (Lambda omega ,Omega ) or Omega subseteq digamma (omega ,Omega ). We apply our results to acquire the solutions of fractional evolution equations and certain types of integral equations. We demonstrate our results with examples, and plot approximate and exact solutions with errors.

Extensions of Orthogonal p-Contraction on Orthogonal Metric Spaces

Fixed-point theory and symmetry are major and vigorous tools to working nonlinear analysis and applications, specially nonlinear operator theory and applications. The subject of examining the presence and inimitableness of fixed points of self-mappings defined on orthogonal metric spaces has become very popular in the latest decade. As a result, many researchers reached more relevant conclusions. In this study, the notion of ϕ-Kannan orthogonal p-contractive conditions in orthogonal complete metric spaces is presented. W-distance mappings do not need to satisfy the symmetry condition, that is, such mappings can be symmetrical or asymmetrical. Self-distance does not need to be zero in w-distance mappings. The intent of this study is to enhance the recent development of fixed-point theory in orthogonal metric spaces and related nonlinear problems by using w-distance. On this basis, some fixed-point results are debated. Some explanatory examples are shown that indicate the currency of the hypotheses and grade of benefit of the suggested conclusions. Lastly, sufficient cases for the presence of a solution to nonlinear Fredholm integral equations are investigated through the main results in this study.

Solutions for nonhomogeneous fractional (p,q)-Laplacian systems with critical nonlinearities

AbstractIn this article, we aimed to study a class of nonhomogeneous fractional (p,q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities inRN{{\mathbb{R}}}^{N}. By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the same approach. Finally, we obtain the corresponding existence results for the fractional (p,q)-Laplacian systems in the case ofN=sp=lqN=sp=lq. It is worth pointing out that using fixed point argument to seek solutions for a class of nonhomogeneous fractional (p,q)-Laplacian systems is the main novelty of this article.

Suzuki Type Common Fixed Point Result on h-Metric Space

In this paper, we defined a general form of the type of Suzuki functions on h-metric space to obtain a common fixed point. Our results generalized some results from the literature.

Fixed Soft Points on Parametric Soft Metric Spaces

This manuscript is devoted to investigating the existence of fixed soft points under conditions in the parametric soft metric spaces. Since the parametric soft metric spaces are the parametric expansions of the parametric metric and soft metric spaces, the observations of the fixed-point results are meaningful to consider in such spaces.

On Numerical Analysis of Bio-Ethanol Production Model with the Effect of Recycling and Death Rates under Fractal Fractional Operators with Three Different Kernels

The main metabolism of yeasts produces bioethanol. Bioethanol, which is produced from biomass and bioenergy crops, has been promoted as one of the most viable alternatives to fossil fuels. The following reaction represents all of the knowledge we have regarding intracellular reactions and their regulatory mechanisms: biomass+substrates→ethanol+biomass(morecells). Atangana has suggested new operators based on a combination of fractional and fractal calculus. Fractal-fractional operators (FFOs) have frequently been utilized to investigate the dynamics of a physical problem. In this paper, FFOs are used to investigate a nonlinear mathematical model for ethanol production with three different kernels. Famous fixed point results are employed to show the existence and uniqueness of the solution of the FFO ethanol model under the Mittag–Leffler kernel. The concept of non-linear analysis is utilized to demonstrate the model’s Ulam–Hyres stability. The Adams—Bashforth numerical technique, which is based on the Lagrangian interpolation method, is utilized to find the solution of the model under fractal-fractional operators with three different kernels. The numerical results are simulated with MATLAB-17 for several sets of fractional orders and fractal dimensions to show the relationship between components of ethanol production under new operators in various senses.