• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• Korean Journal of English Language and Linguistics
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• v.3 no.1
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• pp.89-108
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• 2003

As pronouns are resolved with their antecedents, definite NPs may enter into the anaphora-antecedent relations with indefinite NPs. This paper is to provide faster and more efficient computational algorithms by which definite NPs are resolved effectively, For this purpose, this paper extends Chierchia's Binding Theory in Categorial Grammar, and definite NPs are resolved with their antecedents by similar algorithms that are used to reflexive resolution. In these algorithms, the relations between indefinite NP and definite NP are represented with λ-expressions, and definite NPs are resolved with their antecedent by λ-conversions.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.211-219
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• 1997

In [6] we proved that if a nals X is reflexive, then $X = W_X + V_X$ . In this paper we show that, for a split nals $X = W_X + V_X$, X is reflecxive if and only if $V_X$ and $W_X$ are reflcxive.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.233-241
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• 1996

The study of non-self-adjoint operator algebras on Hilbert space was only beginned by W.B. Arveson[1] in 1974. Recently, such algebras have been found to be of use in physics, in electrical engineering, and in general systems theory. Of particular interest to mathematicians are reflexive algebras with commutative lattices of invariant subspaces.

• 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.

• East Asian mathematical journal
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• v.26 no.3
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• 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.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.71-77
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• 2006

We find the ${\epsilon}$-fuzzy equivalence relation generated by the union of two ${\epsilon}$-fuzzy equivalence relations on a set, find the ${\epsilon}$-fuzzy equivalence relation generated by a fuzzy relation on a set, and find sufficient conditions for the composition ${\mu}{\circ}{\nu}$ of two ${\epsilon}$-fuzzy equivalence relations ${\mu}$ and ${\nu}$ to be the ${\epsilon}$-fuzzy equivalence relation generated by ${\mu}{\cup}{\nu}$. Also we study fuzzy partitions of ${\epsilon}$-fuzzy equivalence relations.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.85-98
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• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].