Some φ-Fixed Point Results for (F,φ,α-ψ)-Contractive Type Mappings with Applications

Mohammad Imdad,Abdur Khan,Waleed Alfaqih,Hayel Saleh

doi:10.3390/math7020122

Mohammad Imdad, Abdur Khan + Show 2 more

Open Access

https://doi.org/10.3390/math7020122

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Abstract

In this paper, we introduce the notions of (F, φ , α - ψ )-contractions and (F, φ , α - ψ )-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness φ -fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.

Highlights

Metric fixed point theory is a very interesting and rapidly growing domain in mathematics.Especially, this theory has fruitful applications in various domains of sciences such as: Physics, Chemistry, Computer Siences, Economics and several others
The most important result of this theory is the celebrated contraction principle essentially due to Banach [1]. This principle states that every self contraction mapping T defined on a complete metric space ( X, d) has a unique fixed point
To introduce the concepts of (F,φ,α-ψ)-contraction mappings and (F,φ,α-ψ)-weak contraction mappings in metric spaces; to establish some φ-fixed point theorems in metric spaces which generalize the corresponding results contained in [2,5,6,7] ; to deduce some fixed point theorems in the setting of partial metric spaces which extend the results contained in [5,6], to examine the existence of solution of a second order ordinary differential equation

Summary

Introduction

Metric fixed point theory is a very interesting and rapidly growing domain in mathematics. The most important result of this theory is the celebrated contraction principle essentially due to Banach [1] This principle states that every self contraction mapping T defined on a complete metric space ( X, d) has a unique fixed point. To introduce the concepts of (F,φ,α-ψ)-contraction mappings and (F,φ,α-ψ)-weak contraction mappings in metric spaces; to establish some φ-fixed point theorems in metric spaces which generalize the corresponding results contained in [2,5,6,7] ; to deduce some fixed point theorems in the setting of partial metric spaces which extend the results contained in [5,6], to examine the existence of solution of a second order ordinary differential equation

Mathematical Preliminaries

Main Results

Results on partial metric spaces

Application to Nonlinear Ordinary Differential Equations

Methods