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.
Highlights
In 2010, the notion of modular metric space was introduced by Chistyakov [3]
In 2012, Wardowski characterized the idea of F-contraction which generalized the Banach contraction principle in various manners and he utilized the new concept of contraction to find the fixed point theorem [15]
We establish a common fixed point theorems for several multivalued F-proximinal mappings in regular modular metric space
Summary
In 2010, the notion of modular metric space was introduced by Chistyakov [3]. In 2012, Wardowski characterized the idea of F-contraction which generalized the Banach contraction principle in various manners and he utilized the new concept of contraction to find the fixed point theorem [15]. Mongkolkeha et al proved the existence of common fixed points for a generalized weak contractive mapping in modular spaces. In 2014, Abdou et al studied the existence of fixed points for contractive-type multivalued maps in the setting of modular metric spaces [1].
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