Some Applications via Coupled Fixed Point Theorems for (????, ????)-H-Contraction Mappings in Partial b- Metric Spaces

Abstract

This work establishes unique common coupled fixed point theorems for given mapping in complete partial b-metric spaces with the concept of (α, ϕ)-H-contraction in the context of partial b-metric spaces. (α, ϕ)-H-contraction

Furthermore, we show how the results may be used and present applications to integral equations and Homotopy theory.

Introduction In previous work, authors have discussed various fixed point theorems on partial b-metric spaces with (ψ, ϕ)-weakly contractive mappings, α−ψ-contractive type, Suzuki type contractions, rational contraction and H-weak contractions. In our work, with the help of (α, ϕ)-H-contraction, we investigated coupled fixed point theorems in partial b-metric spaces.

Objectives: Finding the unique common fixed points for a given mapping in partial b-metric spaces via (α, ϕ)-H-contraction

Methods with the help of α-admissible mapping, H-rational type, (α, ϕ)−H-contraction we have shown coupled fixed point findings in complete partial b-metric spaces

Results: We obtained unique common coupled fixed point results via (α, ϕ)−H-contraction type for the given mapping in complete partial b-metric spaces.

Conclusions: This present study uses contractive mappings of the   H type in the reference of partial b-metric space to give some fixed point results, appropriate examples that illustrate the main findings, In addition, boundary value problems and homotopy applications are given.