Fixed Point Theorems for Hardy--Rogers Type Multivalued Mappings in b-Metric Spaces

Abstract

This paper establishes new existence and uniqueness theorems for p-Hardy-Rogers type multivalued mappings in complete b-metric spaces. Our approach replaces the traditional constant coefficients in the contractive condition with distance-dependent control functions and incorporates a p-order iteration scheme, thereby providing a more general and flexible structure that encompasses a wider class of multivalued operators. Our findings significantly improve and generalize the Hardy-Rogers type fixed point theorems obtained by Chaib et al.(2026) by relaxing the required assumptions, incorporating the h-upper semicontinuity into the hypotheses and considering the p-th iterate of the mapping. Several examples are provided to demonstrate the applicability of our results.