Double controlled M-metric spaces and some fixed point results

Abstract

In this article, we introduce the idea of double controlled M-metric space by employing two control functions a(u,w) and β(w,v) on the right-hand side of the triangle inequality of M-metric space. We provide some examples of double controlled M-metric spaces. We also provide some fixed point results under new type of contractions in the setting of double controlled M-metric spaces. Moreover, we give an example to highlight the importance of one of our main results.

Keywords

• fixed point
• fredholm integral equation
• double controlled m-metric space