Fixed point of multivalued ρ−contractive mappings and their comparison in modular function spaces

Abstract

This paper presents a comprehensive survey on some multivalued ρ−contractive type mappings in the framework of modular function spaces, in which case, existence of fixed points are proved and the various ρ−contractive type mappings considered are compared in the framwork of modular function spaces. Our results complement the results obtained on normed and metric spaces in literature. Also, our method of proof serves as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive and accretive type mappings.