On Certain Fixed Points for (α,φ,F)-Contraction on S_b- Metric Spaces with Applications

Abstract

This work establishes unique fixed point theorems (UFPT) for self mapping in complete S_b-metric spaces (S_b-MS) with the concept of (α,φ,F)-contraction in the context of S_b-MS Furthermore, we show how the results may be used and present applications to integral equations and homotopy theory.

Introduction: In previous work authors were discussed fixed pointon various metric spaces with F -contractions, α-type almost -F- contractions, α-type F -Suzuki contractions, (φ, F)-contraction, F - weak contractions, α −ψ-contractive type, α −ψ-Meir-Keeler contractive mapping, α-ratonal contractive mappings, (α, β) − (φ,ψ)-rational contractive type mappings.

Objectives: Finding the unique fixed point for self mapping in S_b-MS, via (α,φ,F)-contraction.

Methods: with the help of α- admisible mapping, (φ, F)-contraction, α type F -contraction and (α.φ,F)-contraction we have fixed point findings in complete S_b-metric spaces.

Results: we obtained unique fixed point results via (α,φ,F) contractive type for self mapping in complete S_b-MS.

Conclusions:  In this article, Contractive mappings of the (α,φ,F) type are used to show certain fixedpoint results in the context of S_b-MS, along with appropriate example that illustrate the key findings. Appications to integral equations and homotopy are also offered.