• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.421-436
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• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.51-65
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• 2011

In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

• East Asian mathematical journal
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• v.27 no.5
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• pp.527-538
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of an equilibrium problem, the set of fixed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for ${\alpha}$-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.481-491
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• 2008

In this paper, we introduce and analyze a new class of generalized mixed equilibrium-like problems. By using the auxiliary principle technique, we suggest three iterative algorithms for the generalized mixed equilibrium-like problem. Under certain conditions, we establish the convergence of the iterative algorithms. Our results extend, improve and unify several known results in this field.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1179-1194
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• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1263-1275
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• 2010

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.

• East Asian mathematical journal
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• v.29 no.3
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• pp.303-314
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• 2013

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.297-327
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• 2019

In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.765-777
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• 2016

In this paper, we propose a new modied Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.