• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.689-700
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• 2006

In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.489-499
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• 2004

In this paper, we introduce and study a new system of nonlinear variational inequalities. The existence and uniqueness of solution for this problem are proved and an iterative algorithm for approximating the solution of system of nonlinear variational inequalities is constructed.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.319-324
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• 2009

In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.493-506
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• 2005

In this paper, we study the behavior and sensitivity analysis of the solution set for a system of parametric generalized nonlinear mixed quasi-variational inclusions in Banach spaces. By using some new and innovative technique, existence theorem for the system of parametric generalized nonlinear mixed quasi-variational inclusions in $L_p(p\ge2$ spaces is established. Our results improve the known result of Agarwal et al.[1].

• 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.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.553-564
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• 1996

Since Giannessi [5] introduced the vector variational inequality in a finite dimensional Euclidean space with further application, Chang et al. [17], Chen et al. [1-4] and Lee et al. [10-16] have considered several kinds of vector variational inequalities in abstract spaces and have obtained existence theorems for their inequalities.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.603-615
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• 1997

In this paper, we introduce and study a new class of random completely generalized nonlinear variational inclusions with non-compact valued random mappings and construct some new iterative algorithms. We prove the existence of random solutions for this class of random variational inclusions and the convergence of random iterative sequences generated by the algorithms.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.579-592
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• 2000

We study the variational principle for quantum unbounded spin systems interacting via superstable and regular interactions. We show that the (weak) KMS state constructed via the thermodynamic limit of finite volume Green's functions satisfies the Gibbs variational equality.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.693-702
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• 2009

In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.