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

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

Abstract:

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 .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:949141

DOI: 10.1155/2012/949141

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