Meir Keeler's Fixed-Point Theorem in Complex-Valued Modular Metric Space

In this paper, we introduce the notion of Meir-Keeler contraction mapping, which is defined in complex-valued modular metric space. Some properties of sequences in this space, which are convergence, Cauchyness and completeness, are used to prove the fixed-point theorem under this mapping. Additionally, the Delta_2-type condition is also defined as the sufficient condition in order to have a unique fixed point.