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This paper introduces the concept of proximal (α , F) -contractions in F -metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. [ABSTRACT FROM AUTHOR]

In this publication, our objective was to introduce and establish the concepts of KGm-contraction and generalized (a, KGm)-contraction in complete Gm-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis. [ABSTRACT FROM AUTHOR]

In this paper, we solve the existence and uniqueness of a solution for a fractional differential equation by introducing some new fixed point results for rational (αβ)-contractions in the framework of orthogonal F-metric spaces. We derive some well-known results in literature as consequences of our leading result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some fixed point results using JS-G-contraction on G-metric spaces, also to prove some fixed point results on Gb-complete metric space for a new contraction. Our results extend and improve some results in the literature. Moreover, some examples are presented to illustrate the validity of our results.

The aim of this paper is to define a Berinde type ( ρ , μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to obtain common fixed point results in b-metric spaces for generalized rational contractions involving control functions of two variables. We provide an example to show the originality of our main result. As outcomes of our results, we derive certain fixed and common fixed point results for rational contractions presuming control functions of one variable and constants. As an application, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

Metric fixed-point theory has become an essential tool in computer science, communication engineering and complex systems to validate the processes and algorithms by using functional equations and iterative procedures. The aim of this article is to obtain common fixed point results in a bicomplex valued metric space for rational contractions involving control functions of two variables. Our theorems generalize some famous results from literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the context of bicomplex valued metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a generalized (α, ΘF)-contraction in the context of an orthogonal F-complete metric space and obtain some new fixed point results for this newly introduced contraction. A nontrivial example is also provided to satisfy the validity of the established results. As consequences of our obtained results, we derive the leading results in [Fixed Point Theory Appl., 2015,185, 2015] and [Symmetry, 2020, 12,832]. As an application, we investigate the existence and uniqueness of the solution for a nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results on complex-valued extended b-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended b-metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of F-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of F-metric space equipped with a directed graph G are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to establish some common fixed point results for generalized contractions including some precise control functions of two variables in the setting of controlled metric spaces. As consequences of our leading results, we derive common fixed point and fixed point results for contractions with control functions of one variable and constants. We also discuss controlled metric spaces endowed with a graph and obtain some common fixed point results in this newly introduced space. As an application of our leading result, we examine the solution of a Fredholm type integral equation. [ABSTRACT FROM AUTHOR]