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

Mariatul Kiftiah; Yudhi Yudhi

doi:10.37905/euler.v12i1.25126

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

Mariatul Kiftiah, Yudhi Yudhi

Abstract

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.

Keywords

Meir-Keeler; Complex; Modular; Metric

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References

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DOI: https://doi.org/10.37905/euler.v12i1.25126