Search

We study the split fixed point problem with multiple output sets in nonlinear spaces, particularly in CAT(0) spaces. We modify the existing self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in the settings of generalized structures. We also present the consequences of our main theorem in terms of the split feasibility problem and the split common fixed point problem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the novel concept of generalized distance denoted as J θ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J θ (u , H ★) , a generalized Hausdorff type distance and a P J θ -property of a pair (H ★ , K ★) of nonempty subsets of extended b-metric space (U ★ , ρ θ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples. [ABSTRACT FROM AUTHOR]

This article introduces a novel iterative process, denoted as F ★ , designed for the class of generalized α -Nonexpensive mappings. The study establishes strong and weak convergence theorems within the context of Banach spaces, supported by carefully chosen assumptions. The convergence results contribute to the theoretical foundation of iterative processes in functional analysis. The presented framework is applied to address nonlinear integral equations, showcasing the versatility and applicability of the proposed F * for the class of generalized iteration process. Additionally, the article includes numerical examples that not only validate the theoretical findings but also provide insights into the practical utility of the developed methodology. [ABSTRACT FROM AUTHOR]

This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate the relationship between integral-type contractions and the generalized dynamic process. The fixed-point results for multivalued mappings that satisfy both the integral Khan-type contraction and the integral θ -contraction are established in a complete metric space. Furthermore, some corollaries are derived based on our main contribution. To demonstrate the novelty of our findings, several examples are provided. Finally, we look into whether nonlinear fractional differential equations have solutions utilizing the obtained results. [ABSTRACT FROM AUTHOR]

We consider the Banach space C [ 0 , 1 ] , which is a symmetric Banach space, and prove the existence and approximation of numerical solutions for a broad class of third-order BVPs. Our approach is based on an integral operator that is constructed using Green's function. The Banach contraction principle (BCP) is applied to guarantee a unique solution to our problem. Moreover, in order to find the value of the numerical solution, this new operator is embedded within the three-step Noor iterative scheme; we named this new iterative scheme the Noor–Green iterative scheme. We provide a convergence theorem for the proposed scheme by employing suitable restrictions on the parameters involved in the problem and in the scheme. The results of the stability of our scheme are also reported. It is worth mentioning that unlike the concept of stability in the classical sense, our result for stability is based on the concept of weak w 2 stability. In order to support our findings, we carried out various numerical experiments using different third-order BVPs. Finally, we report on the application of our iterative scheme to solve a class of fractional BVPs in the same symmetric Banach space. Our results are essentially new in the present literature and extend several of the results found in the current literature. [ABSTRACT FROM AUTHOR]

The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation's solution. [ABSTRACT FROM AUTHOR]

In order to solve issues that arise in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization issues, equilibrium problems, complementarity issues, selection and matching problems, and issues proving the existence of solutions to integral and differential equations, fixed point theory provides vital tools. In this study, we discuss topological structure and several fixed-point theorems in the context of generalized neutrosophic cone metric spaces. In these spaces, the symmetric properties play an important role. We examine the existence and a uniqueness of a solution by utilizing new types of contraction mappings under some circumstances. We provide an example in which we show the existence and a uniqueness of a solution by utilizing our main result. These results are more generalized in the existing literature. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The major aim of this article is to show how to estimate direct errors using the J iteration method. Direct error estimation of iteration processes is being investigated in different journals. We also illustrate that an error in the J iteration process can be controlled. Furthermore, we express J iteration convergence by using distinct initial values. [ABSTRACT FROM AUTHOR]

In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F ⊥ -Suzuki-type ( F ⊥ -ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this manuscript, we defined (α, F)-contractions in the context of double-controlled metric spaces and partially ordered double-controlled metric spaces. We established new fixed-point results and defined the notion of double-controlled metric space on a Reich-type contraction. Our findings are generalizations of a few well-known findings in the literature. Some non-trivial examples and certain consequences are also provided to illustrate the significance of the presented results. The existence and uniqueness of the solution of non-linear fractional differential equations and the monotone iterative method are also determined using the fixed-point method. [ABSTRACT FROM AUTHOR]

In this article, we develop a faster iteration method, called the A ∗ ∗ iteration method, for approximating the fixed points of almost contraction mappings and generalized α -nonexpansive mappings. We establish some weak and strong convergence results of the A ∗ ∗ iteration method for fixed points of generalized α -nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w 2 -stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra–Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature. [ABSTRACT FROM AUTHOR]

The idea of best proximity points of the fuzzy mappings in fuzzy metric space was intorduced by Vetro and Salimi. We introduce a new type of proximal contractive condition that ensures the existence of best proximity points of fuzzy mappings in the fuzzy complete metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing Ψ , Φ -fuzzy proximal contractions and Ψ , Φ -fuzzy proximal interpolative contractions. The obtained results improve and generalize many best proximity point theorems published earlier. Moreover, we provide many nontrivial examples to validate our best proximity point theorem. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce an ordered implicit relation that can be used for the existence of fixed points of new contractions defined in cone A-metric spaces. We investigate a fixed-point method for proving the existence of Urysohn integral equation solutions. We prove an homotopy result by the application of obtained fixed-point theorem. The hypothesis is demonstrated with examples. [ABSTRACT FROM AUTHOR]

In this paper, the theory of symmetric q-calculus and conic regions are used to define a new subclass of q-starlike functions involving a certain conic domain. By means of this newly defined domain, a new subclass of normalized analytic functions in the open unit disk E is given. Certain properties of this subclass, such as its structural formula, necessary and sufficient conditions, coefficient estimates, Fekete–Szegö problem, distortion inequalities, closure theorem and subordination results, are investigated. Some new and known consequences of our main results as corollaries are also highlighted. [ABSTRACT FROM AUTHOR]