Some fixed point results for relation theoretic weak φ -contractions in cone metric spaces equipped with a binary relation and application to the system of Volterra type equations

Abstract

In this paper, some fixed point results for relation theoretic weak φ-contractions on cone metric spaces which is defined over a Banach algebra and equipped with a binary relation are proved. These results extend and generalize several results of metric and cone metric spaces. Some examples are provided which demonstrate the results proved herein. An application of our main result to a system of Volterra type equations is given.