Best proximity point theorems by K, C and \mathcal{MT} types in b-metric spaces with an application

In this paper, we introduce the concept of weak \mathcal{MT}-K rational cyclic and weak \mathcal{MT}-C  rational cyclic conditions and a combination of both conditions in what we call weak \mathcal{MT}-KC rational cyclic condition. We investigate some best proximity points theorems for a pair of mappings that satisfy these conditions that have been established in b-metric spaces. Our results include an application to the nonlinear integral equation as well.

Keywords:

b-metric space , mathcal{MT}-function , Rational cyclic condition , Cyclic map , best proximity point