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

Document Type : Research Paper

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

3 Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran

Abstract

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