• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.373-388
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• 2015

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.237-260
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• 2001

The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.777-786
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• 2013

The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

• 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.3_4
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• pp.603-619
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• 2011

To the best of our knowledge, it would probably be the first time in the literature that we clarify the relationship between Yamada's method and viscosity iteration correctly. We design iterative methods based on the hybrid steepest descent algorithms for solving variational inclusions, equilibrium problems. Our results unify, extend and improve the corresponding results given by many others.

• East Asian mathematical journal
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• v.26 no.3
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• pp.389-395
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• 2010

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2887-2893
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• 1996

Governing equations infrictional contact problems are introduced using variational inequality formulations which are regularized to overcome the diffculties of non-differentiability of the friction functional. Also finite element approximations and a priori error estimations are derived based on those formulations. Numerical simulations are performed illustrating the theoretical results.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.531-543
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• 2014

The object of the present paper is to discuss some interesting properties of analytic functions f(z) associated with the subclasses $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$. Also, radius problems of $\frac{1}{\delta}f({\delta}z)$ for f(z) in the class $\mathcal{D}({\beta}_1,{\beta}_2,{\beta}_3;{\lambda})$, $\mathcal{G}({\theta},{\alpha})$ and $\mathcal{Q}({\theta},{\alpha})$ are considered.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.188-192
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• 2002

The ellipsoid algorithm solves some feasibility(or optimization) problems with LMI(Linear Matrix Inequality) constraint in polynomial time. Recently, it has been replaced by interior point algorithm due to its slow convergence and incapability of verifying feasibility. This paper proposes a method to improve its convergence by using the deep-cut method of linear programming. Simulation results show that the improved algorithm is more effective than the original one.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.