Perov multivalued contraction pair in rectangular cone metric spaces

Abstract

Perov studied the Banach contraction principle in the framework of a generalized metric space and presented Perov contraction condition where the contractive constant is replaced by a matrix with nonnegative entries and spectral radius less than 1. Azam et al. presented the notion of rectangular cone metric space following the idea of Branciari, Huang and Zhang by replacing the triangular inequality in the cone metric space by rectangular inequality. Motivated by the work of Abbas and Vetro and Radenovi´c, the purpose of this paper is to introduce a new class of Perov type multivalued mappings and present a common fixed point result for such mappings on a complete rectangular cone metric space. Furthermore, an example is also presented to demonstrate the validity of our results. Our results extend, unify and generalize various comparable results in the existing literature.