• 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.

• International journal of steel structures
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• v.18 no.5
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• pp.1654-1665
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• 2018

In an irregular prism tensegrity, the number of force equilibrium equations is less than the number of unknown parameters of nodal coordinates and member force ratios. As a result, the form-finding process normally becomes nonlinear with additional conditions or needs to be carried out with the use of iterative procedures. For cases of irregular prism tensegrity which involves large number of members, it was found that previously proposed methods of form-finding are not practical. Moreover, there is a need for a form-finding approach which is able to cater to different requirements on final configuration. In this paper, the length relation condition is introduced to be used in combination with the force equilibrium equation. With the combined use of length relation and equilibrium conditions, a linear form-finding approach for irregular prism tensegrity was successfully formulated and developed. An easy-to-use interactive form-finding tool has been developed which can be used for form-finding of irregular prism tensegrities with large number of elements as well as under diverse specific requirements on their configurations.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.533-555
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• 2022

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.

• Journal of the military operations research society of Korea
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• v.8 no.2
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• pp.57-68
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• 1982

Bimatrix games are the two-person non-zero-sum non-cooperative games. These games were studied by Mills, Lemke, Howson, Millham, Winkels, and others. This paper is a systematic and synthetic survey relevant to bimatrix games. Among the many aspects of researches on bimatrix games, emphasis in this paper is placed on the relation of the equilibrium set to Nash subsets. Topics discussed are as follows: Properties of equilibrium point; The structure of equilibrium set; Relation of Nash subsets to equilibrium set; Algorithm for finding the equilibrium points; Concepts of solutions on bimatrix games.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.375-388
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• 2013

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.

• Architectural research
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• v.17 no.1
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• pp.31-40
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• 2015

A simple force-finding process based on an optimization technique is proposed for tensegrity structures. For this purpose, the inverse problem of form-finding process is formulated. Therefore, the position vector of nodes and element connectivity information are provided as priori. Several benchmark tests are carried out to demonstrate the performance of the present force-finding process. In particular, the force density distributions of simplex tensegrity are thoroughly investigated with the important parameters such as the radius, height and twisting angle of simplex tensegrity. Finally, the force density distribution of arch tensegrity is produced by using the present force-finding process for a future reference solution.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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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.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.495-524
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• 2016

In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

• 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.

• Journal of Industrial Technology
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• v.15
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• pp.203-208
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• 1995

This paper suggests the three dimensional steady state searching techniques of hard disk/head system, which has some skew angle with flexure. In order to analyze the steady state behaviors of magnetic head slider, the localized Knudsen number and the localized bearing numbers are sued. For finding the steady state of magnetic head slider under the pre-loaded condition, I proposed multi-dimensional Newton-Raphson method which traces the equilibrium position of magnetic head slider, which has 3-degrees of freedom, using Jacobian matrix. The multi-dimensional Newton-Raphson method is very efficient technique for finding the steady state position of magnetic head slider because it approaches to the equilibrium position with changing three parameters simultaneously.