• 대한수학회보
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• 제33권1호
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• pp.45-55
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• 1996

Recently, Giannessi [1] introduced a vector variational inequalityy for vector-valued functions in an Euclidean space. Since then, Chen et al. [2-6], Lee et al. [7], and Yang [8] have intensively studied vector variational inequalities for vector-valued functions in abstract spaces.

• East Asian mathematical journal
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• 제22권1호
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• pp.1-16
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• 2006

Some new reverses of the Schwarz inequality in inner product spaces and applications for vector-valued sequnces and integrals are given.

• 충청수학회지
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• 제28권1호
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• pp.13-28
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• 2015

In this paper, we use two mappings satisfying certain expansive conditions to construct convergent sequences in complex valued metric spaces, and then we prove that the limits of the convergent sequences are the points of coincidence or common fixed points for the two mappings. The main theorems in this paper are the generalizations and improvements of the corresponding results in real metric spaces, cone metric spaces and topological vector space-valued cone metric spaces.

• 대한수학회지
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• 제56권6호
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• pp.1515-1528
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• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• 한국수학사학회지
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• 제26권4호
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• 대한수학회보
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• 제34권2호
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• pp.273-285
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• 1997

The aim of this paper is to present theorems on the exitence of zeros for mappings defined on convex subsets of topological vector spaces with values in a vector space. In addition to natural assumptions of continuity, convexity, and compactness, the mappings are subject to some geometric conditions. In the first theorem, the mapping satisfies a "Darboux-type" property expressed in terms of an auxiliary numerical function. Typically, this functions is, in this case, related to an order structure on the target space. We derive an existence theorem for "obtuse" quasiconvex mappings with values in an ordered vector space. In the second theorem, we prove the existence of a "common zero" for an arbitrary (not necessarily countable) family of mappings satisfying a general "inwardness" condition againg expressed in terms of numerical functions (these numerical functions could be duality pairings (more generally, bilinear forms)). Our inwardness condition encompasses classical inwardness conditions of Leray-Schauder, Altman, or Bergman-Halpern types.

• East Asian mathematical journal
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• 제33권1호
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.203-207
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• 2008

In [1], Mishra and Wang established relationships between vector variational-like inequality problems and non-smooth vector optimization problems under non-smooth invexity in finite-dimensional spaces. In this paper, we generalize recent results of Mishra and Wang to infinite-dimensional case.

• 한국지능시스템학회논문지
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• 제8권5호
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• pp.1-4
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• 1998

The main goal of this paper is to investigate some properties of the locally convex fuzzy topological vector space.