A General Iterative Approach to Variational Inequality Problems and Optimization Problems. (30th November 2010)

• Record Type: Journal Article
• Authors: Jung, Jong Soo
• Other Names: Yao Jen Chih Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2011(2011)
• Publication Date: 2010-11-30
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2011/284363
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We introduce a new general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space and then establish strong convergence of the sequence generated by the proposed iterative scheme to a common element of the above two sets under suitable control conditions, which is a solution of a certain optimization problem. Applications of the main result are also given.