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

Abstract

In this paper, we consider bv(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 bv(s)-metric spaces and explore some of their properties. We provide proofs of the Banach contraction principle in strong bv(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.