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

<p>In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of <italic>k</italic>-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.</p>
</abstract>

In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.

Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Department of Mathematics, Comsats Institute of Information Technology, Lahore 54000,

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and...

Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Publié en ligne: 23 déc. 2016

Pages: 79 - 96

Reçu: 25 mai 2016

Accepté: 26 sept. 2016

DOI: https://doi.org/10.1515/aupcsm-2016-0007

Mots clés
fixed point, strict pseudo-contraction, equilibrium problem, variational inequality problem, inverse strongly monotone mapping, shrinking projection method

© 2016 Muhammad Aqeel Ahmad Khan, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Publié en ligne: 23 déc. 2016

Pages: 79 - 96

Reçu: 25 mai 2016

Accepté: 26 sept. 2016

DOI: https://doi.org/10.1515/aupcsm-2016-0007

Mots clésfixed point, strict pseudo-contraction, equilibrium problem, variational inequality problem, inverse strongly monotone mapping, shrinking projection method

© 2016 Muhammad Aqeel Ahmad Khan, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Mots clés
fixed point, strict pseudo-contraction, equilibrium problem, variational inequality problem, inverse strongly monotone mapping, shrinking projection method