Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations

This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ-contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ-contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations.