• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.29-35
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• 2010

In this note, we will prove a new equilibrium existence theorem for a compact acyclic strategic game by using Begle's fixed point theorem.

• 한국태양에너지학회:학술대회논문집
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• 2009.11a
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• pp.161-167
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• 2009

The liquid solar air conditioning system is introduced as an alternative solution to control air condition and to save electrical energy consumption. The heat and mass transfer performances of dehumidifier/regenerator in liquid solar air conditioning system are influenced by air and desiccant condition. The application of this system, the thermal energy from the sun and inlet air are unable to control, but operation parameter of other components such as pump, fan and sensible cooling unit are able to control. The equilibrium point of heat and mass transfer are the liquid desiccant and inlet air conditions, where, the heat and mass are not transferred between the liquid desiccant and vapor air. By knowing equilibrium point of heat and mass transfer, the suitable optimal desiccant conditions for certain air condition are funded. This present experiment study is investigated the equilibrium point heat and mass transfer in various air and desiccant temperature. The benefit of equilibrium point heat and mass transfer will be helpful in choose and design proper component to optimize electrical energy consumption.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.467-478
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• 2016

In this paper, we propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of split feasibility, fixed point problems and equilibrium problems of quasi-nonexpansive mappings. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility, fixed point problems and equilibrium problems. An example is given to illustrate the main result of this paper.

• 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.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.777-798
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• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.749-759
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• 2012

A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.

• 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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.10
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• pp.80-89
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• 1996

This paper proposes a new COA (center of area) defuzzifier that is working in the accurate and fast manner. The proposed COA defuzzifier involves both membership values and the spans of membership functions in clauclating a crisp value. In additon, it avoid division by replacing the COA calculation with the searching of the momentum equilibrium point. The moment equilibrium point is searched in the coarse-to-fine manner such that the moment computing points during the coarse searching are moved in the interval of fuzzy terms until they are reached at two adjacent fuzzy terms searching method accerlates the finding of the moment equilibrium point by O(M) mazimally when compared iwth the equal interval searching method of ruitz. In order to verify the accuracy of the proposed COA defuzzifier, the crisp values obtained form the proposed coarse-to-fine searching are compared with the precise crisp values from the arithmetic calculation. Application to the truck backer-upper control problem of the proposed COA defuzzifier is presented. The control performance is compared with that of the conventional COA defuzzifier in tems of the average tracing distance.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.301-307
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• 2003

The purpose of this paper is to give a generalization of the quasi fixed-point theorem due to Lefebvre, and prove a new existence theorem of equilibrium in a generalized quasi-game.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.