Strong convergence of a hybrid method for pseudomonotone variational inequalities and fixed point problems

Xin Yu; Yonghong Yao; Yeong-Cheng Liou

doi:10.2478/v10309-012-0033-4

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Strong convergence of a hybrid method for pseudomonotone variational inequalities and fixed point problems

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 1 (May 2012)

By: Xin Yu, Yonghong Yao and Yeong-Cheng Liou

Open Access

|May 2013

Abstract

In this paper, we suggest a hybrid method for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known methods: extragradient method and CQ method. We derive a necessary and sufficient condition for the strong convergence of the sequences generated by the proposed method.

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