Approximating Solutions of Matrix Equations via Fixed Point Techniques
Rahul Shukla,
Rajendra Pant,
Hemant Kumar Nashine,
Manuel De la Sen
Affiliations
Rahul Shukla
Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Rajendra Pant
Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Hemant Kumar Nashine
Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa
Manuel De la Sen
Faculty of Science and Technology, Institute of Research and Development of Processes IIDP, University of the Basque Country, Barrio Sarriena, 48940 Leioa, Bizkaia, Spain
The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.
