Optimal proximity fixed point in entire G-metric spaces with applications

This work discusses the optimal proximity fixed point theorem applicable to non-self-mappings within complete G-metric spaces. The study defines the essential and adequate conditions for the existence of such points. There is also a fixed-point theorem in the paper that is based on the main finding. Then, the theoretical results are applied to analytic functions of a complex variable, showing how useful these abstract results can be in real life. The paper demonstrates that theorems related to best proximity and fixed points can be applied in areas beyond pure mathematics in more than just pure mathematics. It makes new connections that extend beyond pure mathematics and into other areas of analytical and applied mathematics. This study brings new ideas and ways to use them to the field of applied mathematics. This work introduces new ideas and methods for their application in the field.