Approximating the fixed points of Suzuki's generalized non-expansive map via an efficient iterative scheme with an application

Pub Date : 2024-03-29 DOI:10.5556/j.tkjm.56.2025.5261
Pragati Gautam, Chanpreet Kaur
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Abstract

This paper is aimed at proving the efficiency of a faster iterative scheme called $PC^*$-iterative scheme to approximate the fixed points for the class of Suzuki's Generalized non-expansive mapping in a uniformly convex Banach space. We will prove some weak and strong convergence results. It is justified numerically that the $PC^*$-iterative scheme converges faster than many other remarkable iterative schemes. We will also provide numerical illustrations with graphical representations to prove the efficiency of $PC^*$ iterative scheme. As an application of the solution of a fractional differential equation is obtained by using $PC^*$ iterative scheme.
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通过高效迭代方案逼近铃木广义非展开映射的定点及其应用
本文旨在证明一种名为"$PC^*$-迭代方案 "的更快迭代方案在均匀凸巴纳赫空间中逼近铃木广义非展开映射类定点的效率。我们将证明一些弱收敛和强收敛结果。数值证明了$PC^*$迭代方案的收敛速度快于许多其他显著的迭代方案。我们还将通过图解提供数值说明,以证明$PC^*$迭代方案的效率。作为一个应用,我们使用$PC^*$迭代方案求得了分数微分方程的解。
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