Year: 2024
Type: article
Abstract: 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
Source: Journal of Mathematical Analysis
Institution: Thammasat University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W3036360299