MONOTONE SUZUKI-MEAN NONEXPANSIVE MAPPINGS WITH APPLICATIONS

Abstract

In this paper, we introduce a new class of monotone generalized nonexpansive mappings and we establish some weak and strong convergence theorem for a newly proposed iterative process in the frame work of an ordered Banach space. This class of mappings is wider than the class of nonexpansive mappings, mean nonexpansive mappings and mappings satisfying condition (C). In addition, we establish that our newly proposed iterative process is faster than some existing iterative process in the literature. Finally, we provide an application to the space of L1([0, 1]) and to nonlinear integral equations. The results obtained in this paper improve, extend and unify some related results in the literature.