Abstract
We present the concept of multivalued mappings in generalized modular metric spaces (GMMS). In addition, we give Caristi and Feng-Liu fixed point results for this type of mappings in GMMS. Then, we obtain an application for final outcomes in the sense of Jleli and Samet.
Highlights
Multivalued mappings have many applications in pure and applied mathematics
We describe two topologies and linked open balls in the generalized modular metric spaces (GMMS)
After that we compare some other topologies in modular spaces, modular metric spaces, and JS(Jleli-Samet)-metric spaces defined by Jleli and Samet in [1]
Summary
Multivalued mappings have many applications in pure and applied mathematics. Topology, theory of functions of a real variable, nonlinear functional analysis, the theory of games, and mathematical economics are some examples for those mentioned areas. We describe two topologies and linked open balls in the generalized modular metric spaces (GMMS). We give a generalization of the Banach principle of contraction mappings and we explain how we find a fixed point if we have a multivalued contraction mapping of a GMMS XD into the nonempty D-closed and bounded subsets of XD. Nadler initiated the fixed point theory of set-valued contractions. After that it is developed by many authors in different directions. The pair ( X, D ) is said to be a generalized modular metric space(GMMS).
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