Journal of Mathematics and Statistics

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

Sahar Mohamed Ali Abou Bakr

DOI : 10.3844/jmssp.2017.88.97

Journal of Mathematics and Statistics

Volume 13, Issue 2

Pages 88-97

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.

Copyright

© 2017 Sahar Mohamed Ali Abou Bakr. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.