On Certain Applications via (𝜑, ℘) -Suzuki type Fixed Point Results in 𝐴𝑏-Metric Spaces

Abstract

Objective: In this study, we establish the existence and uniqueness of the common coupled fixed point theorem on complete - metric space. Method: We have used the - type Suzuki contraction on two mappings. Findings: For two mappings on the complete -Metric Space, we were able to obtain and prove a unique common coupled fixed point theorem and justify it with a suitable example. Novelty: A unique common coupled fixed point is obtained by using -type Suzuki contraction on two mappings and application of Suzuki contractive fixed point solutions of - type to integral equations in the setup of -Metric Space. Subject classification for mathematics in 2000. 54E50, 47H10, and 54H25. Keywords: Ab -Metric Space; -Type Suzuki Contraction; -Compatible; Ab -Completeness; Coupled Fixed Point