12 Results Found

This paper introduces novel, non-classical Julia and Mandelbrot sets using the Jungck–Noor iterative method with s-convexity, and derives an escape criterion for higher-order complex polynomials of the form $z^n+\Im z^3-\Re z+\omega$, w...

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 Gr...

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalize...

In this paper, an efficient decomposition method is constructed and used for solving system of nonlinear equations. The method based on the decomposition technique of Noor [M.A.Noor, K.I.Noor, Some iterative schemes for nonlinear equations, Appl. Mat...

In this paper, we introduce a fast iterative scheme and establish its convergence under a contractive condition. This new scheme can be viewed as an extension and generalization of existing iterative schemes such as Picard–Noor and UO iterative schem...

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated fixed-point methods have been introduced. The main aim of th...

In this paper, we introduce a new three-step iterative scheme for finding the common solutions of the variational inequality using the technique of updating the solution. We suggest, iterative algorithms involving three-steps for the predictor-correc...

In this paper, we introduce a new class of Bregman generalized $\alpha$ -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman gene...

In this paper, we propose a new three-step iterative scheme to approximate fixed points of contraction operators in Banach spaces. Under standard Lipschitz conditions, we establish the existence, uniqueness, and strong convergence of the iterative se...

This study focuses on a three-step iterative scheme, referred to as the NIP iteration, for the approximation of fixed points associated with nonexpansive mappings in uniformly convex Banach spaces. Weak convergence is established using Fejér m...

In 2009, Noor and Waseem studied an important third-order iterative method. The convergence order is obtained using Taylor expansion and assumptions on the derivatives of order up to four. In this paper, we have obtained convergence order three for t...

Background: Age-related Macular Degeneration (AMD) is a leading cause of irreversible vision loss, particularly in the elderly. Optical Coherence Tomography (OCT), a noninvasive imaging modality, is widely used for retinal disease detection. However,...