Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

Abstract

Abstract In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

Keywords

• Coupled fixed point
• Strong coupled fixed point
• Contraction conditions
• Fuzzy cone metric space