Fixed point theorems in a new type of modular metric spaces

Abstract

In this paper, considering both a modular metric space and a generalized metric space in the sense of Jleli and Samet (Fixed Point Theory Appl. 2015:61, 2015), we introduce a new concept of generalized modular metric space. Then we present some examples showing that the generalized modular metric space includes some kind of metric structures. Finally, we provide some fixed point results for both contraction and quasicontraction type mappings on generalized modular metric spaces.

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Modulars from Nakano onwards

“…We close this subsection mentioning the paper Turkoglu, Manav [145], where a new type of modular metric space has been introduced. 4.6.…”

Common fixed point for some generalized contractive mappings in a modular metric space with a graph

“…It is clear that if ω satisfies the 2 -type condition, then ω satisfies the 2 -condition, and that the converse is not true. Throughout this paper, we consider the modular metrics satisfying the 2 -type condition, and we adopt the definitions of some topological notions as stated in [11]. Definition 1.5 Let ω be a modular metric on X.…”