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In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld's hypothesis for the He atom. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]

Food security is a basic human right that guarantees humans an adequate amount of nutritious food. However, plant viruses and agricultural pests cause real damage to food sources, leading to negative impacts on meeting the human right of obtaining a sufficient amount of food. Understanding infectious disease dynamics can help us to design appropriate control and prevention strategies. Although cassava is among the most produced and consumed crops and greatly contributes to food security, cassava mosaic disease causes a decrease in photosynthesis and reduces cassava yield, resulting in a lack of crops. This paper developed a fractional model for cassava mosaic disease (CMD) dynamics based on the Caputo–Fabrizio (CF) fractional derivative to decrease cassava plant infection. We used fixed-point theory to study the existence of a unique solution in the form of the CMD model. A stability analysis of the model was conducted by using fixed-point theory and the Picard technique. A new numerical scheme was proposed for solving the nonlinear system of a fractional model in the sense of the CF-derivative and applied to obtain numerical simulations for a fractional model of the dynamics of CMD. The obtained results are described using figures that show the dynamics and behaviors of the compartments of CMD, and it is concluded that decreasing the population of whitefly vectors can prevent cassava plants from becoming infected better than increasing the recovery rate of the infected cassava plants. [ABSTRACT FROM AUTHOR]

This paper introduces a novel F fixed-point iteration method that leverages Green's function for solving the nonlinear Troesch problem in Banach spaces, which are symmetric spaces. The Troesch problem, characterized by its challenging boundary conditions and nonlinear nature, is significant in various physical and engineering applications. The proposed method integrates fixed-point theory with Green's function techniques to develop an iteration process that ensures convergence, stability, and accuracy. The numerical experiments demonstrate the method's efficiency and robustness, highlighting its potential for broader applications in solving nonlinear differential equations in Banach spaces. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵ 2 u = f (u , ▵ u) on an annular domain Ω in R N with the Navier boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : R + × R − → R + is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f (ξ , η) to have superlinear or sublinear growth on ξ , η as | (ξ , η) | → 0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]

After the initiation of Jachymski's contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing literature. As an application of our leading result, we explore the existence and uniqueness of solutions of the Volttera integral equation of the second kind. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings on a complete G-metric space is itself a generalized F-contraction mapping on a space of compact sets. We also present several examples in 2-D and 3-D for our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a direct problem and an inverse problem involving a nonlinear fractional diffusion equation, which can be applied to many physical situations. The equation contains a Caputo fractional derivative, a symmetric uniformly elliptic operator and a source term consisting of the sum of two terms, one of which is linear and the other is nonlinear. The well-posedness of the direct problem is examined and the results are used to investigate the stability of an inverse problem of determining a function in the linear part of the source. The main tools in our study are the generalized eigenfunction expansions theory for nonlinear fractional diffusion equations, contraction mapping, Young's convolution and generalized Grönwall's inequalities. We present a stability estimate for the solution of the inverse source problem by means of observation data at a given point in the domain. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlocal fractional coupled system of (k , ψ) -Hilfer fractional differential equations, which involve, in boundary conditions, (k , ψ) -Hilfer fractional derivatives and (k , ψ) -Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel'skiĭ's fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples. [ABSTRACT FROM AUTHOR]

The concept referred to as the measure shadowing property for a dynamical system on compact metric space has recently been introduced, acting as an extension of the classical shadowing property by using the property of the Borel measures on the phase space. In this paper, we extend the concept of the measure shadowing property of continuous flows from compact metric spaces to the general metric spaces and demonstrate the equivalence relation between the measure shadowing property and the shadowing property for flows on metric spaces via the shadowable points. [ABSTRACT FROM AUTHOR]

Fractals are a common characteristic of many artificial and natural networks having topological patterns of a self-similar nature. For example, the Mandelbrot set has been investigated and extended in several ways since it was first introduced, whereas some authors characterized it using various complex functions or polynomials, others generalized it using iterations from fixed-point theory. In this paper, we generate Mandelbrot sets using the hybrid Picard S-iterations. Therefore, an escape criterion involving complex functions is proved and used to provide numerical and graphical examples. We produce a wide range of intriguing fractal patterns with the suggested method, and we compare our findings with the classical S-iteration. It became evident that the newly proposed iteration method produces novel images that are more spontaneous and fascinating than those produced by the S-iteration. Therefore, the generated sets behave differently based on the parameters involved in different iteration schemes. [ABSTRACT FROM AUTHOR]

This paper is devoted to showing the relevance of the notion of completeness used to establish a fixed point theorem in fuzzy metric spaces introduced by Kramosil and Michalek. Specifically, we show that demanding a stronger notion of completeness, called p-completeness, it is possible to relax some extra conditions on the space to obtain a fixed point theorem in this framework. To this end, we focus on a fixed point result, proved by Mihet for complete non-Archimedean fuzzy metric spaces (Theorem 1). So, we define a weaker concept than the non-Archimedean fuzzy metric, called t-strong, and we establish an alternative version of Miheţ's theorem for p-complete t-strong fuzzy metrics (Theorem 2). In addition, an example of t-strong fuzzy metric spaces that are not non-Archimedean is provided. [ABSTRACT FROM AUTHOR]

Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam's notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzdȩk's fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): F ξ 1 3 + ξ 2 3 3 + F ξ 1 3 − ξ 2 3 3 = 2 F (ξ 1) + 2 F (ξ 2) , 2 F ξ 1 3 + ξ 2 3 2 3 = F (ξ 1) + F (ξ 2) for all ξ 1 , ξ 2 ∈ R . [ABSTRACT FROM AUTHOR]

Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided. [ABSTRACT FROM AUTHOR]

This article introduces the concept of generalized (ff F , b , ϕ ˘) contraction in the context of b -metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued (ff F , b , ϕ ˘) contractions in partially ordered b -metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems. [ABSTRACT FROM AUTHOR]

Under the effect of the Rosenblatt process, the well-posedness and Hyers–Ulam stability of nonlinear fractional stochastic delay systems are considered. First, depending on fixed-point theory, the existence and uniqueness of solutions are proven. Next, utilizing the delayed Mittag–Leffler matrix functions and Grönwall's inequality, sufficient criteria for Hyers–Ulam stability are established. Ultimately, an example is presented to demonstrate the effectiveness of the obtained findings. [ABSTRACT FROM AUTHOR]

This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric  S b -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations. [ABSTRACT FROM AUTHOR]

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model's intricate dynamics. [ABSTRACT FROM AUTHOR]

In this manuscript, we discuss fractional fuzzy Goursat problems with Caputo's g H -differentiability. The second-order mixed derivative term in Goursat problems and two types of Caputo's g H -differentiability pose challenges to dealing with Goursat problems. Therefore, in this study, we convert Goursat problems to equivalent systems fuzzy integral equations to deal properly with the mixed derivative term and two types of Caputo's g H -differentiability. In this study, we utilize the concept of metric fixed point theory to discuss the existence of a unique solution of fractional fuzzy Goursat problems. For the useability of established theoretical work, we provide some numerical problems. We also discuss the solutions to numerical problems by conformable double Laplace transform. To show the validity of the solutions we provide 3D plots. We discuss, as an application, why fractional partial fuzzy differential equations are the generalization of usual partial fuzzy differential equations by providing a suitable reason. Moreover, we show the advantages of the proposed fractional transform over the usual Laplace transform. [ABSTRACT FROM AUTHOR]

We develop the local convergence of the six order Contraharmonic-mean Newton's method (CHN) to solve Banach space valued equations. Our analysis approach is two fold: The first way uses Taylor's series and derivatives of higher orders. The second one uses only the first derivatives. We examine the theoretical results by solving a boundary value problem also using the examples relating the proposed method with other's methods such as Newton's, Kou's and Jarratt's to show that the proposed method performs better. The conjugate maps for second-degree polynomial are verified. We also calculate the fixed points (extraneous). The article is completed with the study of basins of attraction, which support and further validate the theoretical and numerical results. [ABSTRACT FROM AUTHOR]

In the field of metric fixed point theory, there are several generalized or modified types of metric space. One such type is called multiplicative metric space. It was initially introduced as a modified version of the metric space, but was later found to be equivalent to the metric space. However, it allows the researchers to view the concept of metric space from a different perspective. Consequently, the idea of product-operated metric space is introduced in this article, which is obtained by removing the slackness of the multiplicative metric space. This article also presents some fundamental characteristics of the product-operated metric space and investigates the existence of fixed points for self-maps in product-operated metric spaces. [ABSTRACT FROM AUTHOR]

In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions. [ABSTRACT FROM AUTHOR]

In the context of a complete metric space, the most important fixed-point result for multi-valued operators was given in 1969. Many extensions of this fixed-point principle for multi-valued operators were proved by different authors. Based on some of the above-mentioned results, we introduce the notion of the multi-valued Feng–Liu-type operator and we construct an abstract fixed-point theory for this general class of multi-valued operators. Our results extend and complement some theorems in metric fixed-point theory for multi-valued operators. An application to a Cauchy problem related to a first-order differential inclusion is also given. In this case, our theorem improves several previous theorems on this subject by relaxing the contraction-type condition (with respect to its second argument) on the multi-valued right-hand side. [ABSTRACT FROM AUTHOR]

This article aims to use various fixed-point techniques to study the stability issue of the impulsive Volterra integral equation in the sense of Ulam–Hyers (sometimes known as Hyers–Ulam) and Hyers–Ulam–Rassias. By eliminating key assumptions, we are able to expand upon and enhance some recent findings. [ABSTRACT FROM AUTHOR]

In this study, we delve into the examination of Finite Time Stability (FTS) within a specific class of Fractional-Order Systems (FOS) with time delays. By applying a fixed-point theorem, we establish novel sufficient conditions to ensure FTS for time-delayed FOS within  1 < σ < 2 . Moreover, we investigate the existence and uniqueness of global solutions for this particular system. To demonstrate the credibility of our results, we substantiate our findings through the presentation of two illustrative examples. [ABSTRACT FROM AUTHOR]