Fixed Circle Theory for Multivalued Mappings with Bilateral Type Contractions

Abstract

This paper investigates the fixed-circle problem in metric spaces within the framework of multivalued mappings. We introduce three novel classes of bilateral contractions, namely, the Jaggi-type bilateral, Dass-Gupta type I bilateral, and Dass-Gupta type II bilateral multivalued contractions, each specifically formulated to extend the fixed-circle theory to the setting of multivalued mappings. By employing these generalized contractive conditions, we establish several fixed-circle and fixed-disc theorems and further extend our results to encompass integral-type contractions. The theoretical findings are supported by illustrative examples that confirm the applicability and robustness of the proposed approach.