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In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.

Numerous strong and weak convergence results on variational inequality problems are known in the literature. We here study a variational inequality problem by using the viscosity approximation method in the nonlinear CAT(0) space, where some novel theorems are established for strong and Δ-convergent sequences.

In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.

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.

Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form QC(p)=apn+mp+c, where n≥2. It establishes escape criteria that play a vital role in generating these sets and provides escape time results using different iterative schemes. In addition, the study includes the visualization of graphical images of Julia and Mandelbrot sets, revealing distinct patterns. Furthermore, the study also explores the impact of parameters on the deviation of dynamics, color, and appearance of fractals.

Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order ς≥0 and ϱ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.

Abstract The main aim of this paper is to study distance spaces, to provide some useful remarks with examples regarding distance spaces, and to establish multiple fixed point results for a C-distance space in the presence of different contractive conditions. This concept allows us to reduce the multidimensional case to a one-dimensional case.

In this article, we consider a wider class of nonexpansive mappings (locally related quasi-nonexpansive) than monotone nonexpansive mappings. We obtained the convergence of fixed point for quasi ϱ-preserving locally related quasi-nonexpansive mappings in hyperbolic space. An iterative process is also used to obtain the convergence results for this mapping. Fixed point is approximated numerically in a nontrivial example by using Matlab.

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s-distance spaces under θ,ϕ,ψ-type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S-iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.

In this article, we consider an extensive class of monotone nonexpansive mappings and introduce a new iteration algorithm to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the framework of hyperbolic space. Faster convergence and stability results are proved for that iteration; also, fixed point is approximated numerically in a nontrivial example by using MATLAB.

Fixed points of monotone α-nonexpansive and generalized β-nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.