Common fixed point theorems in C*-algebra-valued generalized metric spaces

The study of common fixed points in generalized metric structures is a dynamic field with significant implications for nonlinear analysis. This paper aims to broaden the scope of fixed point theory by investigating coincidence and common fixed points within the recently introduced framework of C*-algebra-valued generalized metric spaces. Unlike classical metric settings, these spaces utilize the power of operator theory to provide more flexible contractive conditions. We establish several common fixed point theorems for a pair of self-mappings satisfying novel C*-algebraic contractive inequalities. By relaxing the requirements on the underlying metric structure and the commutativity of the mappings, our results unify and significantly extend various existing findings in the literature, including those in C*-algebra-valued metric and b-metric spaces. Each main result is supported by a concrete example, carefully chosen to situate our contributions within the existing literature and to underscore the added generality of our framework.