Generalized Contractive Mappings and Fixed-Point Theorems in Complete G-Metric Spaces

This paper establishes existence and uniqueness theorems for fixed points in complete G-metric spaces under new contractive conditions. Our approach utilizes a parameter α∈[0,2] and a function mapping into a finite subset of [0,1/2), incorporating various G-metric distances between points and their images. A primary contribution of this work is the identification and rectification of critical logical flaws and gaps in the proofs presented in previous studies. By providing a more rigorous analytical framework, we re-establish the fixed-point results and extend them to include the iterates of the mapping. These results strengthen the theoretical foundation of fixed-point theory in generalized metric structures.