Fixed point theorems in a new type of modular metric spaces

Abstract

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.

Keywords

• Fixed point
• Fatou property
• Modular metric spaces
• Generalized metric spaces
• Quasi-contraction