New Fixed Point Theorems in Orthogonal &#x0D; &#x0D; &#x0D; F&#x0D; &#x0D; &#x0D; -Metric Spaces with Application to Fractional Differential Equation

Hamid Baghani,Manuel De La Sen,Tanzeela Kanwal,Azhar Hussain

doi:10.3390/sym12050832

Abstract

We present the notion of orthogonal F -metric spaces and prove some fixed and periodic point theorems for orthogonal ⊥ Ω -contraction. We give a nontrivial example to prove the validity of our result. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

Highlights

Introduction and PreliminariesFixed point theory is one of the important branches of nonlinear analysis
Banach contraction principle [1], a number of authors have been working in this area of research
Jleli and Samet [16] presented the idea of F -metric space and proved an analogue of Banach contraction principle [1]

Summary

Introduction and Preliminaries

Fixed point theory is one of the important branches of nonlinear analysis. After the celebrated. Metric fixed point theory grew up after the well-known Banach contraction theorem. Jleli and Samet [16] presented the idea of F -metric space and proved an analogue of Banach contraction principle [1]. They introduced a collection F defined below and presented the idea of generalized metric space called F -metric space: Definition 1 ([16]). Let F be the set of functions ζ : (0, ∞) → R satisfying the following conditions:.

Fixed Point Theorem

Periodic Point Theorem

Application