Fixed Point Theorems for Mappings Satisfying Weak Nonexpansivity Condition (Weak Contractivity Condition) into (from) Cartesian Products Normed Spaces

Abstract

This paper suggests new types of weak nonexpansive mappings defined from normed space X into its Cartesian product X × X, studies the main features of the fixed points for those mappings and extends the concept of (C)-contractivity condition introduced in some previous research papers. On other side, it introduces new types of contraction mappings with a mixed monotone property; the {a, b, c} M-first type and the {a, b, c} M-second type contractions, these types are defined from the Cartesian product space X × X into X, where X is a sequentially ordered Banach space, proves the existence of first-anti-second and second-anti-first couple fixed points of such types and generalizes some of the results given before.