Mutual Contraction Principles in Strong $b_v(s)$ Metric Spaces: Implications for Generalized Metrics

Abstract

In this paper, we consider $b_v(s)$-metric spaces, introduced as a generalization of metric spaces, rectangular metric spaces, $b$-metric spaces, rectangular $b$-metric spaces, and $v$-generalized metric spaces. Next, we introduce the concept of strong $b_v(s)$-metric spaces and explore some of their properties. We provide proofs of the Banach contraction principle in strong $b_v(s)$-metric spaces. Then, we define mutual Reich contraction and present results that generalize many known results in fixed point theory. Finally, we extend these results to a set of operators and prove that equilibrium is a global attractor for any scheme presented in this paper which has numerous applications in dynamical systems.