Fixed point theorems in R-metric spaces with applications

Abstract

The purpose of this paper is to introduce the notion of R-metric spaces and give a real generalization of Banach fixed point theorem. Also, we give some conditions to construct the Brouwer fixed point. As an application, we find the existence of solution for a fractional integral equation.

Keywords

• <i>r</i>-metric spaces
• fixed point
• strong <i>r</i>-compact metric spaces
• fractional integral equations