Iterative algorithm with errors for fixed points of relatively nonexpansive mappings

Abstract

Finding fixed points of nonexpansive mappings is a hot topic in different branches of mathematical and engineering sciences. In this paper, two iterative algorithms with errors are proposed and proved to be strongly convergent to fixed points of relatively of Lyapunov functional and generalized projection operator, etc. Moreover, it is demonstrated how to use the newly obtained iterative algorithms to approximate zero points of maximal monotone operators, which is also an important topic in the related areas.