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

Muhammad Aqeel Ahmad Khan

doi:10.1515/aupcsm-2016-0007

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

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 15 (2016): Issue 1 (December 2016)

By: Muhammad Aqeel Ahmad Khan

Open Access

|Dec 2016

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.

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Articles in this issue

DOI: https://doi.org/10.1515/aupcsm-2016-0007 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 79 - 96

Submitted on: May 25, 2016

Accepted on: Sep 26, 2016

Published on: Dec 23, 2016

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

fixed point,

strict pseudo-contraction,

equilibrium problem,

variational inequality problem,

inverse strongly monotone mapping,

shrinking projection method

Related subjects:

Mathematics,

General mathematics

© 2016 Muhammad Aqeel Ahmad Khan, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 15 (2016): Issue 1 (December 2016)