Abstract and Applied Analysis

Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems

Yeong-Cheng Liou, Yonghong Yao, Chun-Wei Tseng, Hui-To Lin, and Pei-Xia Yang

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We consider a general variational inequality and fixed point problem, which is to find a point x * with the property that (GVF): x * GVI ( C , A ) and g ( x * ) Fix ( S ) where GVI ( C , A ) is the solution set of some variational inequality Fix ( S ) is the fixed points set of nonexpansive mapping S , and g is a nonlinear operator. Assume the solution set Ω of (GVF) is nonempty. For solving (GVF), we suggest the following method g ( x n + 1 ) = β g ( x n ) + ( 1 - β ) S P C [ α n F ( x n ) + ( 1 - α n ) ( g ( x n ) - λ A x n ) ] , n 0 . It is shown that the sequence { x n } converges strongly to x * Ω which is the unique solution of the variational inequality F ( x * ) - g ( x * ) , g ( x ) - g ( x * ) 0 , for all x Ω .

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Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 949141, 15 pages.

First available in Project Euclid: 1 April 2013

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Liou, Yeong-Cheng; Yao, Yonghong; Tseng, Chun-Wei; Lin, Hui-To; Yang, Pei-Xia. Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 949141, 15 pages. doi:10.1155/2012/949141. https://projecteuclid.org/euclid.aaa/1364845183

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