• East Asian mathematical journal
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• 제27권5호
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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.

• Korean Journal of Mathematics
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• 제18권2호
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• pp.105-118
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• 2010

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

• Korean Journal of Mathematics
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• 제27권2호
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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.

• 대한수학회지
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• 제52권6호
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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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• 제28권5_6호
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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.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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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.

• 대한수학회보
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• 제51권2호
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• pp.479-499
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• 2014

In this paper, we propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.

• 대한기계학회논문집
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• 제19권3호
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• pp.820-833
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• 1995

An analysis is performed to examine the equilibrium state and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations. The equilibrium states are found by the steady state solution of the governing equations. In order to investigate the stability of the system about its state in equilibrium, and eigenvalue problem is constructed. As a result, constraints for the coeffieients in the model equations are obtained by the stability condition of the equilibrium state as well as by their physically realizable bounds. It is observed that the models with pressure-strain rate correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium tensor do not behave properly. Stability considerations about three most commonly used models are given in detail in the final section.

• Structural Engineering and Mechanics
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• 제35권4호
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• pp.511-533
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• 2010

As a truly meshfree method, meshless equilibrium on line method (MELM), for 2D elasticity problems is presented. In MELM, the problem domain is represented by a set of distributed nodes, and equilibrium is satisfied on lines for any node within this domain. In contrary to conventional meshfree methods, test domains are lines in this method, and all integrals can be easily evaluated over straight lines along x and y directions. Proposed weak formulation has the same concept as the equilibrium on line method which was previously used by the authors for enforcement of the Neumann boundary conditions in the strong-form meshless methods. In this paper, the idea of the equilibrium on line method is developed to use as the weak forms of the governing equations at inner nodes of the problem domain. The moving least squares (MLS) approximation is used to interpolate solution variables in this paper. Numerical studies have shown that this method is simple to implement, while leading to accurate results.