New Approximation Techniques for Solving Variational Inclusions Problem via SP Iterative Algorithm with Mixed Errors for Accretive Lipschitzian Operators

Kumar, Vivek; Hussain, Nawab

doi:10.22075/ijnaa.2020.4579

New Approximation Techniques for Solving Variational Inclusions Problem via SP Iterative Algorithm with Mixed Errors for Accretive Lipschitzian Operators

Document Type : Research Paper

Authors

Vivek Kumar ¹

Nawab Hussain ²

¹ Department of Mathematics, KLP College,Rewari, Haryana, India

² Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

10.22075/ijnaa.2020.4579

Abstract

Using diﬀerent convergence techniques and under the lack of parametrical restrictions, the convergence and stability results of SP iterative algorithm with mixed errors for accretive Lipschitzian operators in Banach spaces are established. We propose numerical examples to verify eﬀectiveness of new convergence techniques and to show that SP iterative algorithm with mixed errors converges more eﬀectively than the Mann, Ishikawa and Noor iterative algorithms with mixed errors. Moreover, new iterative approximation of solution for variational inclusion problem in Banach spaces is investigated by using SP iterative algorithm with mixed errors for accretive Lipschitzian operators. Our results are improvement and generalization of results of Kim [15], Gu [10], Gu and Lu [11], Chugh and Kumar [7] and many others in the literature.

Keywords

Iterative Schemes

Fixed Point

Stability

Accretive Operators

Variational Inequality