A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces

Qin, Xiaolong; Shang, Meijuan; Su, Yongfu

doi:10.1016/j.na.2007.10.025

Cited by 66 publications

(23 citation statements)

References 15 publications

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“…As applications, we utilize our results to study the optimization problem. Our results improve and extend the corresponding results in [1,[3][4][5].…”

Section: Introductionsupporting

confidence: 89%

See 1 more Smart Citation

Generalized mixed equilibrium problem in Banach spaces

张石生

2009

Appl. Math. Mech.-Engl. Ed.

111

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This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-φ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

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“…As applications, we utilize our results to study the optimization problem. Our results improve and extend the corresponding results in [1,[3][4][5].…”

Section: Introductionsupporting

confidence: 89%

“…Recently, many authors studied the problems of finding a common element of the set of fixed points for a nonexpansive mapping and the set of solutions to an equilibrium problem in the setting of Hilbert space and uniformly smooth and uniformly convex Banach space, respectively (see, for instance, [3][4][5] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Generalized mixed equilibrium problem in Banach spaces

张石生

2009

Appl. Math. Mech.-Engl. Ed.

111

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“…Subsequently, many authors studied the problem of finding a common element in the fixed point set of nonexpansive mappings, in the solution set of variational inequalities and in the solution set of equilibrium problems, for instance see [10][11][12][13][14][15][16][17][18][19][20].…”

Section: T→0 F(tz + (1 − T)x Y) ≤ F(x Y);mentioning

confidence: 99%

Strong convergence of composite general iterative methods for one-parameter nonexpansive semigroup and equilibrium problems

Xin

et al. 2012

J Inequal Appl

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In this paper, we introduce both explicit and implicit schemes for finding a common element in the common fixed point set of a one-parameter nonexpansive semigroup {T(s)|0 ≤ s <∞} and in the solution set of an equilibrium problems which is a solution of a certain optimization problem related to a strongly positive bounded linear operator. Strong convergence theorems are established in the framework of Hilbert spaces. As an application, we consider the optimization problem of a k-strict pseudocontraction mapping. The results presented improve and extend the corresponding results of many others. 2000 AMS Subject Classification: 47H09; 47J05; 47J20; 47J25.

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“…Some methods have been proposed to solve the generalized equilibrium problems and equilibrium problems. See, for example, [1,8,9,11,14,16,17,20,21,24,25,28,30,31,33,37] and the references contained therein.…”

Section: Introductionmentioning

confidence: 99%

Fixed point solutions of variational inequality and generalized equilibrium problems with applications

Shehu

2010

Ann. Univ. Ferrara

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In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solution of generalized equilibrium problem and the set of solutions of the variational inequality problem for a co-coercive mapping in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. Furthermore, new convergence results are deduced and finally we apply our results to solving optimization problems and obtaining zeroes of maximal monotone operators and co-coercive mappings.

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A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces

Cited by 66 publications

References 15 publications

Generalized mixed equilibrium problem in Banach spaces

Generalized mixed equilibrium problem in Banach spaces

Strong convergence of composite general iterative methods for one-parameter nonexpansive semigroup and equilibrium problems

Fixed point solutions of variational inequality and generalized equilibrium problems with applications

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