Some Extended Results for Multivalued <i>F</i>-Contraction Mappings

Abstract

In this study, we introduce a new notion, so-called KW-type F-contraction mapping, inspired by the ideas of Wardowski and Klim–Wardowski. Then, we investigate the existence of a best proximity point for such mappings by considering a new family, which is larger than the family of functions that is often used in fixed-point results for multivalued mappings. To demonstrate the effectiveness of our result, we also give a comparative example to which similar results in the literature cannot be applied. Moreover, we present an application of our main result to homotopic mappings.

Keywords

• <i>F</i>-contraction
• best proximity point
• multivalued mappings