Mann and Ishikawa iterative schemes for fixed points of strongly relatively nonexpansive mappings and their applications

Abstract

Relatively nonexpansive mapping is a kind of important mappings which has a close connection with some problems in the area of image recovery, economics, applied mathematics and engineering sciences. Two kinds of iterative schemes, Mann and Ishikawa iterative schemes, will be investigated for approximating the fixed points of strongly relatively nonexpan-sive mappings in a real smooth and uniformly convex Banach space. Compared to the already existing iterative schemes for strongly relatively nonexpan-sive mappings, these iterative schemes are simple and easy to realize. Some weak convergence theorems are proved, which extend and complement some previous work. Moreover, the applications of the iterative schemes on approximating zero points of maximal monotone operators are demonstrated.