New multivalued contractions and the fixed-circle problem

Abstract

A recent problem, the fixed-circle problem, deals with the geometric properties of the fixed points of a self-mapping (on metric or generalized metric spaces). In this paper, we consider this problem for the multivalued case. We obtain new fixed-circle results on metric spaces by means of the multivalued mappings. We introduce new multivalued contractions using Wardowski's technique and obtain new fixed-circle results with some applications to integral type contractions. We provide necessary illustrative examples in order to support the validity of our obtained results.