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.
Highlights
In 1990, the fixed point theory in modular function spaces was initiated by Khamsi, Kozlowski, and Reich [10]
Fixed point theory in modular metric spaces was studied by Abdou and Khamsi [1]
In this paper, considering both a modular metric space and a generalized metric space in the sense of Jleli and Samet [6], we introduce a new concept of generalized modular metric space
Summary
In 1990, the fixed point theory in modular function spaces was initiated by Khamsi, Kozlowski, and Reich [10]. Fixed point theory in modular metric spaces was studied by Abdou and Khamsi [1]. Their approach was fundamentally different from the one studied in [2, 3]. If we relax the triangle inequality, some of the classical known facts in metric spaces may become impossible to obtain. This is the case with the generalized metric distance introduced by Jleli and Samet in [6]. Ćirić’s fixed point theorem in this new space, we take the contraction constant k. We give the definition of generalized modular metric spaces
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