Fixed Point Results for Generalized F-Contractions in Modular b-Metric Spaces with Applications

Vahid Parvaneh,Maryam Khorshidi,Hassen Aydi,Nawab Hussain,Nabil Mlaiki

doi:10.3390/math7100887

Abstract

The aim of this paper is to generalize the F -contractive condition in the framework of α - ν -complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented. Moreover, an illustrative example and some related applications are presented to support the obtained results.

Highlights

The concept of a b-metric space has been introduced by Bakhtin [1] and Czerwik [2,3]
A modular metric space is an applicable extension of classical modulars over linear spaces
We deal with modular metric spaces as the nonlinear version of the classical one introduced by Nakano [23] on a vector space and a modular function space presented by Musielak [24] and Orlicz [25]

Summary

Introduction

The concept of a b-metric space has been introduced by Bakhtin [1] and Czerwik [2,3]. The pair (Ω, B) is called a b-metric space. A modular metric space is an applicable extension of classical modulars over linear spaces. The concept of a modular metric space has been introduced in [19,20,21,22]. We deal with modular metric spaces as the nonlinear version of the classical one introduced by Nakano [23] on a vector space and a modular function space presented by Musielak [24] and Orlicz [25]

Objectives

Results

Conclusion