Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities. (5th January 2021)

• Record Type: Journal Article
• Authors: Akram, M.; Khan, Aysha; Dilshad, M.
• Other Names: Mursaleen Mohammad Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-05
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6674349
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.