Abstract
In this article, we introduce the notion of complex valued modular metric spaces. We also a prove generalization of Banach Fixed Point Theorem, which is one of the most simple and significant tests for existence and uniqueness of solution of problems arising in mathematics and engineering for complex valued modular metric spaces. In addition, we express some results related to these spaces. Finally, we give an application of our results to digital programming.
Highlights
AND PRELIMINARIESIn 2011, Azam et al [6] introduced the notion of complex valued metric spaces and they gave generalization of Banach contraction mapping principle [10]
In 2008, Chistyakov introduced the notion of modular metric spaces, which has a physical interpretation [11] and he gave the fundamental properties of modular metric spaces [12]
In 2011, Mongkolkeha and et al proved contraction-type ...xed point theorems on modular metric spaces [23]
Summary
AND PRELIMINARIESIn 2011, Azam et al [6] introduced the notion of complex valued metric spaces and they gave generalization of Banach contraction mapping principle [10]. They obtained various ...xed point theorems on this spaces [2, 7, 15, 16, 22, 24, 31, 32, 33, 34]. Mutlu have contributed to develop these structures introducing various ...xed point theorems on modular metric spaces [9, 3, 8, 13, 14, 17, 18, 19, 27, 28]. The aim of this paper is to introduced the concept of complex valued modular metric spaces, which is more general than well-know modular metric spaces, and give some ...xed point theorems under the contraction condition in these spaces.
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