Cone A_b-metric space over real Banach algebra and some results on coupled fixed points

Abstract

In this paper, we expand the notion of a coupled fixed point to encompass mappings on cone A_b-metric space over real Banach algebra, and we establish some coupled fixed point theorems. Our results extend some existing coupled fixed point results on cone A_b-metric space to cone A_b-metric space over real Banach algebra. Our results are generalized enough to contain many interesting results as corollaries. We also provide an example to illustrate the validity of our result.