Certain Applications of New Caristi Contraction Coupled Solution in S𝑏-Metric spaces

Objective: To initiate some new Caristi-type contractions on complete Sb-metric spaces. Methods: Caristi-type contractions of four mappings together with -compatibility in Sb- metric space used to derive some common coupled fixed-point theorems. Findings: We obtained new common coupled fixed-point results in complete Sb- metric spaces by using Caristi-type contractions which generalize some existing results in the literature and validated them with an appropriate example. Novelty: By defining a new Caristi type contraction, we have established a common coupled fixed-point result and have given some applications to integral equations as well as homotopy theory of common coupled fixed point results in Sb- metric spaces.