Generalized coupled common fixed point results in partially ordered A-metric spaces

Abstract

Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S : X3→[0,∞), where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A : Xn→[0,∞) and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.