<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

Published Online: Dec 23, 2016

Page range: 79 - 96

Received: May 25, 2016

Accepted: Sep 26, 2016

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

Keywords
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

Published Online: Dec 23, 2016

Page range: 79 - 96

Received: May 25, 2016

Accepted: Sep 26, 2016

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

Keywordsfixed 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.

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