Mutual contraction principles in strong bv (s) metric spaces: Implications for generalized metrics

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.