A Novel Extension of $S$-Metric Spaces with Application to Solving $n$th-Degree Polynomial Equations

This paper introduces a novel generalization of the classical concept of $S$-metric spaces, referred to as composed $S$-metric spaces. By incorporating a composed function, we impose more general conditions on the triangle inequality, extending the traditional framework. Using this newly defined structure, we establish the existence and uniqueness of fixed points under suitable assumptions. Our results expand upon and generalize several established results in the literature across various types of spaces. To highlight the practical significance of our findings, we provide an example that demonstrate the applicability of the theoretical results. This examples highlight the versatility and effectiveness of composed $S$-metric spaces in a range of mathematical contexts, particularly in solving $n$th degree polynomial equations.