Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces

Hasanen A Hammad,Praveen Agarwal,Juan L G Guirao

doi:10.3390/math9162012

Abstract

In this manuscript, some tripled fixed point results were derived under (φ,ρ,ℓ)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.

Highlights

Fixed point theory is one of the important and indispensable branches of non-linear analysis due to the proliferation of its applications in many disciplines such as engineering, computer science, physics, economics, biology, chemistry, etc
Homotopy theory is a fundamental branch of algebraic topology where topological objects are studied up to homotopy equivalence
Strong links have emerged between this theory and many branches of mathematics

Summary

Introduction

Fixed point theory is one of the important and indispensable branches of non-linear analysis due to the proliferation of its applications in many disciplines such as engineering, computer science, physics, economics, biology, chemistry, etc In mathematics, this technique is credited with clarifying and studying the behavior of dynamical systems, statistical methods, game theory models, differential equations, and many others. Strong links have emerged between this theory and many branches of mathematics This trend plays a prominent role in strengthening ties between homotopy theory and category theory (higher-dimensional), which have received considerable attention in recent years, see [12,13,14,15]. As applications, the existence and uniqueness of the solution to an initial value problem (IVP) and a homotopy theory are discussed

Preliminaries

Theorems and Discussion

Application to IVPs

Application to a Homotopy