ON NEW EXISTENCE OF A UNIQUE COMMON SOLUTION TO A PAIR OF NON-LINEAR MATRIX EQUATIONS

The main goal of this article is to investigate the existence of a unique positive definite common solution to a pair of matrix equations. Our focus will be on two particular types of matrix equation systems. In order to achieve our target, we take the help of elegant properties of Thompson metric on the set of all n × n Hermitian positive definite matrices. To proceed with this, we first derive a common fixed point result for a pair of mappings utilizing a certain class of control functions in a metric space. Then we obtain sufficient conditions to ensure a unique positive definite common solution to the equations. Finally, to validate our results, we provide numerical examples with diagrammatic representations of the convergence behavior of iterative sequences.