Fixed Points of Multivalued Mappings on $S$-Metric Spaces

In the present study, an extension of Bollenbacher and Hicks's fixed point theorem, which is a version of Caristi's fixed point theorem, is proved for the context of multivalued mappings in $S$-metric spaces. Several significant results are derived from this extension. Moreover, it has been shown that various fixed point theorems for single-valued mappings can be derived as special cases from the main theorem.