Hybrid Approximate Proximal Point Algorithms for Variational Inequalities in Banach Spaces

作者：Ceng L C; Guu S M; Yao J C^*

来源：Journal of Inequalities and Applications, 2009, 2009(1): 275208.

DOI：10.1155/2009/275208

Let C be a nonempty closed convex subset of a Banach space E with the dual E*, let T : C -> E* be a continuous mapping, and let S : C -> C be a relatively nonexpansive mapping. In this paper, by employing the notion of generalized projection operator we study the variational inequality (for short, VI (T - f, C)): find x is an element of C such that < y - x, Tx - f > >= 0 for all y is an element of C, where f is an element of E* is a given element. By combining the approximate proximal point scheme both with the modified Ishikawa iteration and with the modified Halpern iteration for relatively nonexpansive mappings, respectively, we propose two modified versions of the approximate proximal point scheme L. C. Ceng and J. C. Yao (2008) for finding approximate solutions of the VI (T - f, C). Moreover, it is proven that these iterative algorithms converge strongly to the same solution of the VI (T - f, C), which is also a fixed point of S.

• 出版日期2009
• 单位中山大学; 上海大学; 上海师范大学