Fixed‐Point Theorems for Multivalued Mappings in Modular Metric Spaces

Abstract

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied.

Common Fixed Point Theorems in Modular Metric Spaces

“…In 2010, V. V. Chistyakov introduced the notation of modular metric spaces [2], he present some interesting applications for superposition operators by applying the theory of modular metric spaces [3]. Later, researchers have studied and extend fixed point problems in modular metric spaces, see for example ( [1], [4], [5], [10], [11], [12]). In this paper we prove some coincidence and common fixed point theorems for a contractive mapping in modular metric spaces.…”

Recent Fixed Point Techniques in Fractional Set-Valued Dynamical Systems

“…Even the studies of modular metric spaces are relatively limited at the time, we suggest that further readings from Refs. [18][19][20] should give some ideas about the theory itself and also how to develop further dynamical systems in this framework.…”

Some Integral Type Weakly Compatible Contraction in Modular Metric Spaces

“…In 2010, V. V. Chistiyakov [12] introduced the more general concept of modular metric spaces. Later, many authors [13,14,15,16,17,18] have extended and generalized the fixed point problems in modular metric spaces.…”