JOURNAL BROWSE
Search
Advanced SearchSearch Tips
STRONG CONVERGENCE OF AN EXTENDED EXTRAGRADIENT METHOD FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
STRONG CONVERGENCE OF AN EXTENDED EXTRAGRADIENT METHOD FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS
Kim, Jong-Kyu; Anh, Pham Ngoc; Nam, Young-Man;
  PDF(new window)
 Abstract
In this paper, we introduced a new extended extragradient iteration algorithm for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of equilibrium problems for a monotone and Lipschitz-type continuous mapping. And we show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.
 Keywords
equilibrium problems;monotone mapping;Lipschitz-type continuous;strong convergence;extragradient algorithm;nonexpansive mapping;
 Language
English
 Cited by
1.
FIXED POINT SOLUTION METHODS FOR SOLVING EQUILIBRIUM PROBLEMS,;;

대한수학회보, 2014. vol.51. 2, pp.479-499 crossref(new window)
1.
Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities, Journal of Optimization Theory and Applications, 2012, 154, 1, 303  crossref(new windwow)
2.
Approximation of Solutions of an Equilibrium Problem in a Banach Space, Journal of Applied Mathematics, 2012, 2012, 1  crossref(new windwow)
3.
Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory and Applications, 2014, 2014, 1, 94  crossref(new windwow)
4.
A Fixed Point Scheme for Nonexpansive Mappings, Variational Inequalities and Equilibrium Problems, Vietnam Journal of Mathematics, 2015, 43, 1, 71  crossref(new windwow)
5.
Weak and strong convergence of hybrid subgradient method for pseudomonotone equilibrium problem and multivalued nonexpansive mappings, Fixed Point Theory and Applications, 2014, 2014, 1, 232  crossref(new windwow)
6.
The subgradient extragradient method extended to equilibrium problems, Optimization, 2015, 64, 2, 225  crossref(new windwow)
7.
A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems, Optimization Letters, 2014, 8, 2, 727  crossref(new windwow)
8.
On asymptotically strict pseudocontractions and equilibrium problems, Journal of Inequalities and Applications, 2013, 2013, 1, 251  crossref(new windwow)
9.
Strong convergence theorems for equilibrium problems involving a family of nonexpansive mappings, Fixed Point Theory and Applications, 2014, 2014, 1, 200  crossref(new windwow)
10.
Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings, Applied Mathematics, 2012, 03, 10, 1357  crossref(new windwow)
11.
On strong convergence of an iterative algorithm for common fixed point and generalized equilibrium problems, Journal of Inequalities and Applications, 2014, 2014, 1, 263  crossref(new windwow)
12.
FIXED POINT SOLUTION METHODS FOR SOLVING EQUILIBRIUM PROBLEMS, Bulletin of the Korean Mathematical Society, 2014, 51, 2, 479  crossref(new windwow)
13.
The extragradient-Armijo method for pseudomonotone equilibrium problems and strict pseudocontractions, Fixed Point Theory and Applications, 2012, 2012, 1, 82  crossref(new windwow)
14.
On variational inequality, fixed point and generalized mixed equilibrium problems, Journal of Inequalities and Applications, 2014, 2014, 1, 203  crossref(new windwow)
15.
HYBRID PROXIMAL POINT AND EXTRAGRADIENT ALGORITHMS FOR SOLVING EQUILIBRIUM PROBLEMS, Acta Mathematica Vietnamica, 2014, 39, 3, 405  crossref(new windwow)
16.
Strong convergence of a Halpern-type algorithm for common solutions of fixed point and equilibrium problems, Journal of Inequalities and Applications, 2014, 2014, 1, 313  crossref(new windwow)
17.
A new iterative method for equilibrium problems and fixed point problems for infinite family of nonself strictly pseudocontractive mappings, Fixed Point Theory and Applications, 2013, 2013, 1, 286  crossref(new windwow)
18.
A New Iterative Method for the Set of Solutions of Equilibrium Problems and of Operator Equations with Inverse-Strongly Monotone Mappings, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
19.
Approximation of solutions to an equilibrium problem in a nonuniformly smooth Banach space, Journal of Inequalities and Applications, 2013, 2013, 1, 387  crossref(new windwow)
20.
On generalized equilibrium problems and strictly pseudocontractive mappings in Hilbert spaces, Fixed Point Theory and Applications, 2014, 2014, 1, 145  crossref(new windwow)
21.
A new iterative scheme with nonexpansive mappings for equilibrium problems, Journal of Inequalities and Applications, 2012, 2012, 1, 116  crossref(new windwow)
22.
Some results on parallel iterative algorithms for strictly pseudocontractive mappings, Journal of Inequalities and Applications, 2013, 2013, 1, 74  crossref(new windwow)
23.
Linesearch Methods for Equilibrium Problems and an Infinite Family of Nonexpansive Mappings, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38, 3, 1157  crossref(new windwow)
 References
1.
P. N. Anh, A logarithmic quadratic regularization method for solving pseudomonotone equilibrium problems, Acta Mathematica Vietnamica 34 (2009), 183-200.

2.
P. N. Anh, An LQP regularization method for equilibrium problems on polyhedral, Vietnam Journal of Mathematics 36 (2008), 209-228.

3.
P. N. Anh, L. D. Muu, V. H. Nguyen, and J. J. Strodiot, Using the Banach contraction principle to implement the proximal point method for multivalued monotone variational inequalities, J. Optim. Theory Appl. 124 (2005), no. 2, 285-306. crossref(new window)

4.
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), no. 1-4, 123-145.

5.
P. Daniele, F. Giannessi, and A. Maugeri, Equilibrium Problems and Variational Models, Kluwer, 2003.

6.
J. K. Kim, S. Y. Cho, and X. Qin, Hybrid projection algorithms for generalized equilibrium problems and strictly pseudocontractive mappings, J. Inequal. Appl. 2010 (2010), Art. ID 312602, 18 pp.

7.
J. K. Kim, S. Y. Cho, and X. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Scientia 31(5) (2011), 2041-2057. crossref(new window)

8.
J. K. Kim and N. Buong, Regularization inertial proximal point algorithm for monotone hemicontinuous mapping and inverse strongly monotone mappings in Hilbert spaces, J. Inequal. Appl. 2010 (2010), Art. ID 451916, 10 pp.

9.
G. M. Korpelevich, An extragradient method for nding saddle points and for other problems, Ekonom. i Mat. Metody 12 (1976), no. 4, 747-756.

10.
P. Kumama, N. Petrot, and R. Wangkeeree, A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions, J. Comput. Appl. Math. 233 (2010), no. 8, 2013-2026. crossref(new window)

11.
G. Li and J. K. Kim, Demiclosedness principle and asymptotic behavior for nonexpan- sive mappings in metric spaces, Appl. Math. Lett. 14 (2001), no. 5, 645-649. crossref(new window)

12.
N. Nadezhkina and W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006), no. 1, 191-201. crossref(new window)

13.
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mapping, Bull. Amer. Math. Soc. 73 (1967), 591-597. crossref(new window)

14.
J. W. Peng, Iterative algorithms for mixed equilibrium problems, strict pseudocontractions and monotone mappings, J. Optim. Theory Appl. 144 (2010), no. 1, 107-119. crossref(new window)

15.
Y. Shehu, Fixed point solutions of generalized equilibrium problems for nonexpansive mappings, J. Comput. Appl. Math. 234 (2010), no. 3, 892-898. crossref(new window)

16.
S. Takahashi and W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007), no.1, 506-515. crossref(new window)

17.
W. Takahashi and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 118 (2003), no. 2, 417-428. crossref(new window)

18.
S. Wang and B. Guo, New iterative scheme with nonexpansive mappings for equilibrium problems and variational inequality problems in Hilbert spaces, J. Comput. Appl. Math. 233 (2010), no. 10, 2620-2630. crossref(new window)

19.
H. K. Xu, Viscosity method for hierarchical fixed point approach to variational inequalities, Taiwanese J. Math. 14 (2010), no. 2, 463-478.

20.
H. K. Xu and T. H. Kim, Convergence of hybrid steepest-descent methods for variational inequalities, J. Optim. Theory Appl. 119 (2003), no. 1, 185-201. crossref(new window)

21.
Y. Yao, Y. C. Liou, and Y. J. Wu, An extragradient method for mixed equilibrium problems and fixed point problems, Fixed Point Theory Appl. 2009 (2009), Art. ID 632819, 15 pp.

22.
L. C. Zeng and J. C. Yao, Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems, Taiwanese J. Math. 10 (2006), no. 5, 1293-1303.