Orthogonal Cone Metric Spaces with Banach Algebras and Fixed Point Theorems of Generalized Lipschitz Mappings

Abstract

In this paper, we impose weaker restriction on generalized Lipschitz constants to prove existence and uniqueness of fixed points in the setting of orthogonal cone metric spaces. Our results extend many of previously obtained findings in literature. Furthermore, we provide two example to support and illustrate the usability of the main results.

Key words and phrases. Orthogonal cone metric space, fixed point, generalized orthogonal contractions, Lipschitz mapping.

2010 Mathematics Subject Classification. 54H25, 47H10