• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.427-439
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• 2014

In this paper, we investigate the ${\alpha}$-well-posedness and ${\alpha}$-L-well-posedness for a mixed vector quasivariational-like inequality using bifunctions. Some characterizations are derived for the above mentioned well-posedness concepts. The concepts of ${\alpha}$-well-posedness and ${\alpha}$-L-well-posedness in the generalized sense are also given and similar characterizations are derived.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1503-1521
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• 2018

The paper introduces a modified subgradient extragradient method for solving equilibrium problems involving pseudomonotone and Lipschitz-type bifunctions in Hilbert spaces. Theorem of weak convergence is established under suitable conditions. Several experiments are implemented to illustrate the numerical behavior of the new algorithm and compare it with a well known extragradient method.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.879-893
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• 2016

In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.337-363
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• 2023

In this paper, we propose a new subgradient extragradient algorithm for finding a solution of monotone bilevel equilibrium problem in reflexive Banach spaces. The strong convergence of the algorithm is established under monotone assumptions of the cost bifunctions with Bregman Lipschitz-type continuous condition. Finally, a numerical experiments is reported to illustrate the efficiency of the proposed algorithm.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.69-82
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• 2010

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically k-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.83-99
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• 2019

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.