Modified inertial Ishikawa iterations for fixed points of nonexpansive mappings with an application

Abstract

This manuscript aims to prove that the sequence {νn} created iteratively by a modified inertial Ishikawa algorithm converges strongly to a fixed point of a nonexpansive mapping Z in a real uniformly convex Banach space with uniformly Gâteaux differentiable norm. Moreover, zeros of accretive mappings are obtained as an application. Our results generalize and improve many previous results in this direction. Ultimately, two numerical experiments are given to illustrate the behavior of the purposed algorithm.

Keywords

• nonexpansive mappings
• accretive mappings
• uniformly gâteaux differentiable norm
• evolution equations