Some fixed point theorems on complex valued modular metric spaces with an application

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 signi…cant 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.

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

“…Next, we recall some basic definitions and fundamental results on complex-valued modular metric space, which was proposed by Ozkan [16].…”

“…The first step involves studying the concept of complexvalued modular metric spaces, as defined by Ozkan in [16], including the definitions, topology, convergent sequences, and fixedpoints. Based on these concepts, the notion of Meir-Keeler ωcontraction mappings is constructed in complex-valued modular metric spaces as previously defined in metric spaces [13], modular spaces [14], and modular metric spaces [15].…”

“…The notion of complex valued modular metric spaces, which is more general than well-known modular metric spaces, was first introduced by Ozkan [16] in 2021. In addition, they showed the generalization of the Banach Fixed-Point Theorem, one of the most important and simple tools for the existence and uniqueness of solutions for problems arising for complex-valued modular metric spaces in the fields of engineering and mathematics.…”

“…However, no work has generalized the fixed-point problem through the Meir Keeler contraction in metric space to complex-valued modular metric space. Inspired by the work of Ozkan in [16], we first introduce a Meir Keeler contraction defined in a complex-valued modular metric space. Our main goal is to investigate the existence and uniqueness of fixed-point of Meir Keeler type mapping in the context of complex-valued modular metric spaces.…”