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

Gui-Xiu Chen,Fatima Abbas,Ahmed Mostafa Khalil,Saif Ur Rehman,Shamoona Jabeen,Arzoo Kanwal,Hayat Ullah

doi:10.1186/s13662-020-03132-8

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.

Highlights

Kirk et al [1] introduced a cyclic contractive type mapping which ensures the existence of the best proximity points in complete metric spaces
We show that μ is a strong coupled fixed point of T
6 Conclusion In this paper, we have introduced the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces

Summary

Introduction

Kirk et al [1] introduced a cyclic contractive type mapping which ensures the existence of the best proximity points in complete metric spaces. 4, we establish some strong coupled fixed point results for the generalized cyclic type fuzzy cone contraction mapping in FCM-space in the sense of Choudhury et al [6]. In the following we prove some coupled fixed point results by partial ordered metric space in FCM-spaces.

Results

Conclusion