New Results of Fixed-Point Theorems and Their Applications in Complete Complex Dc∗-Metric Spaces

Abstract

The first objective of the present manuscript is to introduce the notion of complex-valued Dc∗-metric spaces as generalizing and improving the idea of D∗-metric spaces by using the context of complex-valued metric space and D∗-metric spaces. The principle of contraction mappings has recently been established. Furthermore, the second objective is devoted to establishing various new fixed-point theorems in complete complex-valued Dc∗-metric spaces that are improved and generalized by Azam et al. Banach’s contraction principle and various distinguished outcomes are also presented in the literatures. Additionally, some implementations of common fixed-point theory on complete complex-valued Dc∗-metric spaces have been offered by applying open and closed balls. Additionally, we provide some illustrative examples as an implementation for our main results.