Abstract
In this paper a generalization of a modular metric which is also a generalization of cone metric, is introduced and some of its topological properties are studied. Next, a fixed point theorem in this space is proved and finally by an example, it is proved that the fixed point result of the paper "Ch. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for contraction mapping in modular metric spaces, Fixed Point Theory Appl. (2011)" is not true.
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