Common fixed point theorems for several multivalued mappings on proximinal sets in regular modular space

Abstract

Abstract In this paper, we found a common fixed point for several multivalued mappings on proximinal sets in regular modular metric space. Also, we introduced the notions of conjoint F-proximinal contraction as well as conjoint F-proximinal contraction of Hardy–Rogers-type for several multivalued mappings. Furthermore, we enhanced our results by giving an application in integral equations.

Keywords

• Multivalued mappings
• Conjoint F-contraction
• Δ 2 ${\Delta}_{2}$ -condition and Δ M ${\Delta}_{M}$ -condition