Common fixed point result satisfying rational contraction in complex valued Gb-metric space

Abstract

In recent years, researchers have become increasingly interested in studying fixed point results within complex-valued metric spaces. This is because these spaces are useful for solving complex equations and have unique topological properties. This paper adds to the development of fixed point theory by presenting a common fixed point theorem for selfmappings that meet a rational contraction condition in complex-valued metric spaces. The goal of this work is to generalize and extend existing fixed point results, making them more applicable to advanced systems. To achieve this, we use a detailed analytical approach within complex-valued metric spaces, which provide a more flexible framework than traditional metric spaces. Our method focuses on proving the existence and uniqueness of common fixed points for such mappings, building on earlier theorems in this field. An example is included to show how the results can be applied, proving their validity in mathematical analysis. The findings not only expand but also unify several known results, opening new directions for further study. Mathematically, this research offers stronger tools for working with complex-valued functions and contractions. While this work is mainly theoretical, it lays a foundation for practical applications in areas like quantum mechanics and computational mathematics in the future.