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 $S:X^{3} \rightarrow[0,\infty)$ S : X 3 → [ 0 , ∞ ) , where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric $A: X^{n} \rightarrow[0,\infty)$ A : X n → [ 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.