Convex (<i>α</i>, <i>β</i>)-Generalized Contraction and Its Applications in Matrix Equations

Abstract

This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex (α,β)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for both linear and nonlinear matrix equations. This paper extends the concept to partially ordered geodesic spaces and establishes new existence and convergence results. Illustrative examples are provided to demonstrate the practical relevance of the findings. Overall, this research contributes a novel approach to the field of matrix equations.

Keywords

• matrix equation
• geodesic space
• partial order