Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems

Wang, Shuang; Hu, Changsong; Chai, Guoqiang

doi:10.1016/j.amc.2009.11.036

Cited by 8 publications

(5 citation statements)

References 12 publications

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“…The problem MEP studied in [15][16][17] and the problem GEP studied in [18][19][20] are still the problem (1.1) studied in the literature [5][6][7][8][9][10][11][21][22][23][24] and others.…”

Section: Resultsmentioning

confidence: 99%

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Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

2011

Fixed Point Theory Appl

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In this paper, we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this paper are new, and a few examples illustrating these results are given. Finally, we point out that some 'so-called' mixed equilibrium problems and generalized equilibrium problems in the literature are still usual equilibrium problems.

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Section: Resultsmentioning

confidence: 99%

“…Recently, some authors used iterative method including composite iterative, CQ iterative, viscosity iterative etc. to find a common element in the intersection of EP(f) and F(S); see, e.g., [5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

2011

Fixed Point Theory Appl

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“…(1) Theorem 3.1, Corollary 3.2, Corollary 3.3, and Corollary 3.4 improve and develop the corresponding results, which were obtained recently by many authors in various references, for example, see [2,3,[7][8][9][11][12][13][14][15][16][17][18]24,30]. In particular, we mention that the iterative scheme (3.1) in Theorem 3.1 of [24] is not well defined without the assumption C ± C ⊂ C on a nonempty closed convex subset C of H.…”

Section: F(t N ) = F(t)mentioning

confidence: 98%

A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

Jung

2011

J Inequal Appl

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In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimization problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area.

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“…The equilibrium problem (1.1) includes, as special cases, numerous problems in physics, optimization and economics. Some authors (see [8,10,11,12,14,18]) have proposed useful methods for solving the equilibrium problem (1.1). Below we describe some of them.…”

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confidence: 99%

A new iterative method for generalized equilibrium and constrained convex minimization problems

Yazdi

2020

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The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this paper, we combine the GPA and averaged mapping approach to propose an explicit composite iterative scheme for finding a common solution of a generalized equilibrium problem and a constrained convex minimization problem. Then, we prove a strong convergence theorem which improves and extends some recent results.

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Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems

Cited by 8 publications

References 12 publications

Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

A new iterative method for generalized equilibrium and constrained convex minimization problems

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