Algorithm analysis of solving fixed point of nonexpansive mappings based on runge-kutta method

Year 2023, Volume: 52 Issue: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1567 - 1577, 03.11.2023

Xiangyao Li Li-jun Zhu Mihai Postolache

Abstract

In order to solve the fixed point of nonexpansive mappings, we propose two iterative algorithms based on runge-kutta method. The first algorithm is focused on solving the fixed point problem of a single nonexpansive mapping, and weak convergence has been proved. we suggest the second algorithm by dynamic string-averaging rule. It can be used to find a common fixed point of a family of finite nonexpansive mappings. We show that the second algorithm is bounded perturbations resilient, and it is strongly convergent.

Keywords

nonexpansive mapping, common fixed point, runge-kutta method

Supporting Institution

National Natural Science Foundation of China

Project Number

11861003

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