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

Adrian Nicolae Branga

doi:10.3390/fractalfract6010016

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.

Highlights

IntroductionAfterwards, many authors have obtained fixed point results on cone metric spaces: Radenović and Rhoades [2], Rezapour and Hamlbarani [3], Kadelburg et al [4], Du [5] and the references therein
Liu and Xu [6] introduced the concept of cone metric space over a Banach algebra and proved some fixed point theorems for Lipschitz mappings
We obtain some fixed point results for self-mappings satisfying a contractive condition of this type

Summary

Introduction

Afterwards, many authors have obtained fixed point results on cone metric spaces: Radenović and Rhoades [2], Rezapour and Hamlbarani [3], Kadelburg et al [4], Du [5] and the references therein. Liu and Xu [6] introduced the concept of cone metric space over a Banach algebra and proved some fixed point theorems for Lipschitz mappings. Cosentino and Vetro [10] obtained new fixed point theorems of Hardy-Rogers type for F-contractions in ordered metric spaces. Fernandez et al [26] proposed a unified model of fractional calculus by using a general operator which includes many types of fractional operators They consider some fractional differential equations and solve a general Cauchy problem in this new framework. Fractal Fract. 2022, 6, 16 uniqueness of the solutions for integral equations were presented, one of them being an integral equation of fractional type

Methods

Results

Conclusions