Interpolative Ćirić-Reich-Rus-type best proximity point results with applications

Abstract

In this paper, we introduce the notion of ω-interpolative Ćirić-Reich-Rus-type proximal contraction. We obtain some best proximity point results for these mappings using the concept of ω-admissibility in complete metric spaces. Some best proximity results are extended to partial ordered metric spaces and graphical metric spaces. Several new definitions are presented by considering the special cases of aforementioned results. The application of these results in fixed point theory is also discussed. The acquired results extend ω-interpolative Ćirić-Reich-Rus-type contraction for obtaining fixed points.

Keywords

• complete metric space
• ordered metric space
• graph theory
• interpolative proximal contraction