The Solution of Nonlinear Matrix Equations Using Suzuki Multivalued Fixed Point Theorems in Rectangular M ‐Metric Spaces

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Abstract
This paper establishes new fixed‐point (FP) theorems for Suzuki–Rational ( ψ , ϕ )‐type multivalued contractions in complete rectangular M ‐metric spaces (RM‐MSs). These theorems ensure the existence of fixed points and provide significant insights into the structural properties of such contractions. Furthermore, we derive important results concerning contractions defined on closed balls within RM‐MS. To demonstrate the originality and applicability of our findings, we present illustrative examples that validate the effectiveness of the proposed theorems. Finally, we investigate the solvability of a system of nonlinear matrix equations (NMEs) in the framework of our study. This application highlights the practical relevance of the theoretical developments and their potential for solving real‐world problems.

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