Exploring Collective Extension of Aydi-Lolo-Piri-Rasham Type Contractions on a Closed Ball with Applications

Abstract

The main purpose of this manuscript is to prove some new fixed point theorems for a pair of multi dominated operators involving simulation function that satisfy a novel extension of Aydi-Lolo-Piri-Rasham type locally contractions in the setting of complete partial b-metric spaces. Also new results for multi-ordered dominated mappings and multi-graph dominated mappings are established on a closed ball in such spaces. To back up our findings, we give non-trivial illustrative examples for multi fixed points in partial b-metric spaces. Applications to the system of nonlinear Volterra type integral equations and fractional differential equations are given to show the novelty of our new results. Our hypothesis will be critical to the theory of fixed points. Our findings can be expanded and improved in various ways by employing multiple sorts of mappings in partial b-metric spaces with applications.