Xiangyao Lİ, Li-jun ZHU, Mihai POSTOLACHE

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

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,

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