<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Department of Information Management, Cheng Shiu University, Kaohsiung 883, Taiwan

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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...

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

Published Online: May 17, 2013

Page range: 489 - 504

DOI: https://doi.org/10.2478/v10309-012-0033-4

Keywords
Variational inequality problem, Fixed point problems, Pseudomonotone mapping, Nonexpansive mapping, Extragradient method, CQ method, Projection

This content is open access.

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

Published Online: May 17, 2013

Page range: 489 - 504

DOI: https://doi.org/10.2478/v10309-012-0033-4

KeywordsVariational inequality problem, Fixed point problems, Pseudomonotone mapping, Nonexpansive mapping, Extragradient method, CQ method, Projection

This content is open access.

Keywords
Variational inequality problem, Fixed point problems, Pseudomonotone mapping, Nonexpansive mapping, Extragradient method, CQ method, Projection