Coupled Fixed Points Results for Hardy–rogers Type of Maps With the Mixed Monotone Property Obtained With the Help of a Variational Technique

Abstract

Sufficient conditions have been obtained for the existence and uniqueness of coupled fixed points for Hardy-Rodgers maps with the mixed monotone property in partially ordered metric spaces using a variational technique. The obtained result generalizes and enriches already known results for other types of maps with mixed monotone property. It is shown that in partially ordered metric spaces the maps of Hardy-Rodgers and Reich with mixed monotonic properties do not coincide.