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

Authors : Xiangyao Li, Lijun Zhu, Mihai Postolache

Pages : 1567-1577

View : 108 | Download : 314

Publication Date : 2023-11-03

Article Type : Research Paper

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