<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

Publié en ligne: 17 mai 2013

Pages: 489 - 504

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

Mots clés
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

Publié en ligne: 17 mai 2013

Pages: 489 - 504

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

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

This content is open access.

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