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.
Hakan Karayılan (Tue,) studied this question.