Solution of an Algebraic Linear System of Equations Using Fixed Point Results in C∗-Algebra Valued Extended Branciari Sb-Metric Spaces

This study explores the realm of metric spaces, advancing beyond conventional boundaries by introducing two innovative types of metrics known as generalized Branciari-type metrics. Through exacting examination and exemplification, we shed light on the intricacies of these newly defined metric spaces and their extended versions. By drawing parallels with established theorems such as Banach and Kannan, we unveil corollaries that establish necessary symmetric conditions for the existence and uniqueness of fixed points concerning self-operators within these spaces. The inclusion of illustrative examples not only bolsters our theoretical framework but also underscores the practical relevance of our findings. Furthermore, we utilize our research to address real-world applications, showcasing how our results can be employed to determine the existence of unique solutions for algebraic systems of linear equations, thereby bridging the theoretical and applied aspects of mathematical exploration. Through these interventions, our study significantly contributes to the comprehensive understanding and utilization of all the properties in metric spaces within diverse mathematical contexts.