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In this manuscript, some remarks on the papers [H. A. Hammad, P. Agarwal, S. Momani, and F. Alsharari, Solving a fractional-order differential equation using rational symmetric contraction mappings, Fractal Fract. 5 (2021), 159] and [A. Hussain, F. Jarad, and E. Karapinar, A study of symmetric contractions with an application to generalized fractional differential equations, Adv. Differ. Equ. 2021 (2021), 300] are given. In the light of remarks, we introduce a new property that makes it convenient to investigate the existence of fixed points of the interpolative contractions in the orthogonal metric spaces. We derive several new results based on known contractions from the main theorems. As an application, we resolve a Urysohn integral equation.

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]

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 article, we introduce (Ψ , Φ) -orthogonal interpolative contractions which generalize orthogonal interpolative contractions. We investigate different conditions on the functions Ψ , Φ : (0 , ∞) → (− ∞ , ∞) to show the existence of fixed-points of set-valued (Ψ , Φ) -orthogonal interpolative contractions. Our fixed point results are improvement of several known results in literature. As an application, we resolve a fractional differential equation. [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 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]

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]

The objective of this research is to propose some new fixed point theorems for fuzzy-dominated operators that satisfy a nonlinear contraction on a closed ball in a complete b-multiplicative metric space. Our strategy involves the use of a combination of two distinct kinds of mappings: one belongs to a weaker class of strictly increasing mappings, and the other is a class of dominated mappings. In order to demonstrate the validity of our new findings, we provide instances that are both illustrative and substantial. Finally, in order to illustrate the novelty of our findings, we provide applications that allow us to derive the common solution to integral and fractional differential equations. Our findings have a significant impact on the interpretation of a large number of previously published studies, both present and historical. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper we discuss unique fixed point of mappings satisfying a locally contractive condition on a closed ball in a complete Gd-metric like space. Examples have been given to show the novelty of our work. Our results improve/generalize several well known recent and classical results. [ABSTRACT FROM AUTHOR]

In this paper, an effort has been made to improve the notion of α-Geraghty contraction type mappings and establish some common fixed point theorems for a pair of α-admissible mappings under the improved approach of generalized rational α-Geraghty contractive type condition in a complete metric space. An example has been constructed to demonstrate the novelty of these results. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the investigations of F-contractions. The aim of this article is to extend the concept of Ciric type F-contraction on a closed ball. We presented the notion of F-contraction on a closed ball and introduced a new approach of fixed point theorems for Fcontraction on a closed ball in a complete metric space. Our results are very useful for the contraction of the mapping only on closed ball instead of the whole space. Some comparative examples are constructed which illustrate the superiority of our results. Our results provide extension as well as substantial generalizations and improvements of several well-known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to continue the study of fixed point theory in complete metric spaces. Wardowski [Fixed Point Theory Appl. 2012: 94] introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalize the Banach contraction principle. The aim of this paper is to extend the concept of F-contraction into generalized F-contraction. An example and application are given to illustrate the usability of the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of dualistic contraction of rational type. We prove some fixed point theorems for ordered mappings satisfying above mentioned contraction. We give examples to illustrate the importance of these results. We present an application of our fixed point result to show the existence of solution of integral equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish fixed point results for semi fixed α*-admissible multivalued mappings satisfying generalized locally α*-ψ-contractive conditions in complete dislocated metric space. As an application, we derive some new fixed point theorems for preordered metric space and metric space endowed with a graph. Example has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we present new fixed point theorems for Kannan type Fp-contraction and Kannan type (α η;GFp)-contraction on a closed ball contained in a complete partial metric space. Some comparative examples are constructed to illustrate the significance of these results. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new fixed point results for Ćirić type α-η-GF-contraction in a complete metric space. We extend the concept of F-contraction and introduce the notion Ćirić type α-η-GF-contraction. An example is given to demonstrate the novelty of our work. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for α-η-GF-contraction in a complete metric space. We extend the concept of F-contraction into an α-η-GF-contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results. [ABSTRACT FROM AUTHOR]

In this article, following the approach of F-contractions, we establish a common fixed point theorem for a pair of self-mappings satisfying F-contraction of rational type in complete metric spaces. An example is constructed to illustrate this result. An application to system of integral equations is presented. [ABSTRACT FROM AUTHOR]