Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

Yonghong Yao; Yeol Cho; Yeong-Cheng Liou

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 640-656
  • ISSN: 2391-5455

Abstract

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In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.

How to cite

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Yonghong Yao, Yeol Cho, and Yeong-Cheng Liou. "Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems." Open Mathematics 9.3 (2011): 640-656. <http://eudml.org/doc/269200>.

@article{YonghongYao2011,
abstract = {In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.},
author = {Yonghong Yao, Yeol Cho, Yeong-Cheng Liou},
journal = {Open Mathematics},
keywords = {Variational inclusion; Mixed equilibrium problem; Fixed point; Optimization problem; Nonexpansive mapping; Strong convergence; variational inclusion; mixed equilibrium problem; fixed point; optimization problem; nonexpansive mapping; strong convergence},
language = {eng},
number = {3},
pages = {640-656},
title = {Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems},
url = {http://eudml.org/doc/269200},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Yonghong Yao
AU - Yeol Cho
AU - Yeong-Cheng Liou
TI - Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 640
EP - 656
AB - In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.
LA - eng
KW - Variational inclusion; Mixed equilibrium problem; Fixed point; Optimization problem; Nonexpansive mapping; Strong convergence; variational inclusion; mixed equilibrium problem; fixed point; optimization problem; nonexpansive mapping; strong convergence
UR - http://eudml.org/doc/269200
ER -

References

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