Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph

Abstract

Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.

Keywords

• common fixed point
• perov's type results
• multivalued mapping
• directed graph
• graphic contraction
• cone metric space
• c-sequence