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Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

Kumar Vivek (Department of Mathematics, K.L.P College, Rewari, India), ratheevivek15@yahoo.com
Hussain Nawab (Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia), nhusain@kau.edu.sa
Khan Abdul Rahim (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia), arahim@kfupm.edu.sa
Gürsoy Faik (Department of Mathematics, Adiyaman University, Adiyaman, Turkey), faikgursoy02@hotmail.com

Using different technique and weaker restrictions on parameters, convergence and stability results of an SP iterative algorithm with errors for a strongly accretive Lipschitzian operator on a Banach space are established. Validity of new convergence results is verified through numerical examples and convergence comparison of various iterative algorithms is depicted. As applications of our convergence result, we solve a nonlinear operator equation and a variational inclusion problem. Our results are refinement and generalization of many classical results.

Keywords: Iterative algorithm, fixed point, stability, strongly accretive operator