<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an <italic>α</italic>-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem.</p></abstract>

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem.

An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the...

An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications

Publié en ligne: 04 avr. 2017

Pages: 247 - 266

Reçu: 05 mai 2014

Accepté: 27 juin 2014

DOI: https://doi.org/10.1515/auom-2015-0017

Mots clés
Modified extragradient method, viscosity approximation method, -inverse strongly monotone mapping, sequence of asymptotically nonexpansive mappings, variational inequalities, AF point property

© 2015 Adrian Petruşel et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications

Publié en ligne: 04 avr. 2017

Pages: 247 - 266

Reçu: 05 mai 2014

Accepté: 27 juin 2014

DOI: https://doi.org/10.1515/auom-2015-0017

Mots clésModified extragradient method, viscosity approximation method, -inverse strongly monotone mapping, sequence of asymptotically nonexpansive mappings, variational inequalities, AF point property

© 2015 Adrian Petruşel et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Modified extragradient method, viscosity approximation method, -inverse strongly monotone mapping, sequence of asymptotically nonexpansive mappings, variational inequalities, AF point property