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

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.