Convergence of a refined iterative method and its application to fractional Volterra–Fredholm integro-differential equations

KH Alam, Y Rohen - Computational and Applied Mathematics, 2025 - Springer
Our research introduces an innovative iterative method for approximating fixed points of
contraction map**s in uniformly convex Banach spaces. To validate the stability of this …

Approximation of fixed point and its application to fractional differential equation

S Khatoon, I Uddin, D Baleanu - Journal of Applied Mathematics and …, 2021 - Springer
In this study, we prove some convergence results for generalized α α-Reich–Suzuki non-
expansive map**s via a fast iterative scheme. We validate our result by constructing a …

On a four-step iterative algorithm and its application to delay integral equations in hyperbolic spaces

AE Ofem, JA Abuchu, GC Ugwunnadi, H Işik… - Rendiconti del Circolo …, 2024 - Springer
The purpose of this article is to study A∗ iterative algorithm in hyperbolic space. We prove
the weak w 2-stability, data dependence and convergence results of the proposed iterative …

Stability and convergence of F iterative scheme with an application to the fractional differential equation

J Ali, M Jubair, F Ali - Engineering with Computers, 2020 - Springer
In this paper, we prove that F iterative scheme is almost stable for weak contractions.
Further, we prove convergence results for weak contractions as well as for generalized non …

Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

M Abbas, MW Asghar, M De la Sen - Mathematics, 2022 - mdpi.com
The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to
approximate the fixed point of (b, η)-enriched contraction map** in the framework of …

[HTML][HTML] A four step feedback iteration and its applications in fractals

A Tassaddiq, M Tanveer, M Azhar, W Nazeer… - Fractal and …, 2022 - mdpi.com
Fractals play a vital role in modeling the natural environment. The present aim is to
investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot …

[HTML][HTML] A Novel Fixed-Point Iteration Approach for Solving Troesch's Problem

D Filali, F Ali, M Akram, M Dilshad - Symmetry, 2024 - mdpi.com
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 …

Iterative Stability Analysis for Generalized α-Nonexpensive Map**s with Fixed Points

M Iqbal, A Ali, HA Sulami, A Hussain - Axioms, 2024 - mdpi.com
This article introduces a novel iterative process, denoted as F★, designed for the class of
generalized α-Nonexpensive map**s. The study establishes strong and weak …

[HTML][HTML] A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Map**s with Applications

D Ali, S Ali, D Pompei-Cosmin, T Antoniu… - Fractal and …, 2023 - mdpi.com
Fixed point theory is a branch of mathematics that studies solutions that remain unchanged
under a given transformation or operator, and it has numerous applications in fields such as …

[HTML][HTML] Solving Fractional Volterra–Fredholm Integro-Differential Equations via A** Iteration Method

AE Ofem, A Hussain, O Joseph, MO Udo, U Ishtiaq… - Axioms, 2022 - mdpi.com
In this article, we develop a faster iteration method, called the A∗∗ iteration method, for
approximating the fixed points of almost contraction map**s and generalized α …