Fixed Point Results for <i>F</i>-Contractions in Cone Metric Spaces over Topological Modules and Applications to Integral Equations

Abstract

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integral equations were presented in the last part of the article, one of them being a fractional integral equation.

Keywords

• <i>F</i>-contractions
• fixed point theorems
• integral equations
• topological left modules
• cone metric spaces