In this article, we introduce the notion of an extended rectangular \(S_b\) -suprametric space, a unified framework that simultaneously generalises extended rectangular b-metric spaces, \(S_b\) -metric spaces, and suprametric spaces. By endowing this structure with an arbitrary binary relation and employing simulation functions together with auxiliary comparison functions, we establish new coincidence point and common fixed point theorems for a pair of nonlinear mappings satisfying a hybrid contractive inequality. Our results absorb, refine and extend a substantial number of known fixed point principles. Several non-trivial examples are provided to demonstrate the sharpness of the hypotheses. As applications, we study the existence of solutions for a periodic boundary value problem of ordinary differential equations, for a Volterra–Fredholm integral equation, and for a system of nonlinear matrix equations arising in control theory.
