Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations

Abstract

In this paper a modified Ishikawa iterative process for approximating a common fixed point of a locally asymptotically nonexpansive cosine family is firstly introduced, and then, by using the theory of cosine families and constructing some control conditions, several strong convergence theorems are established for this iterative process in Banach spaces. Moreover, an example is presented to illustrate the main result of the paper.