• 충청수학회지
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• 제30권1호
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• pp.151-157
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• 2017

In this paper we introduce AP-Henstock integral of vector valued functions which is a generalization of Henstock integral of vector valued functions, investigate some of its properties, and characterize AP-Henstock integral of vector valued functions by the notion of equiintegrability.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• 대한수학회지
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• 제37권5호
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• East Asian mathematical journal
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• 제22권1호
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• pp.17-35
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• 2006

Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Banach spaces are given. Applications for complex-valued functions are considered as well.

• 한국산업정보학회논문지
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• 제12권5호
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• 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.

• 대한수학회지
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• 제40권2호
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• pp.207-224
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• 2003

Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.297-336
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• 2018

In this paper we wish to establish some basic properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

• 대한수학회보
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• 제50권6호
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• pp.1915-1922
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• 2013

We prove the admissibility of the space $L_0(\mathcal{A},X)$ of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.

• 대한수학회보
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• 제55권4호
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• pp.1109-1124
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• 2018

For a metric space (X, d) and ${\alpha}$ > 0. We study the structure and properties of vector-valued Lipschitz algebra $Lip{\alpha}(X,E)$ and $lip{\alpha}(X,E)$ of order ${\alpha}$. We investigate the approximate and Character amenability of vector-valued Lipschitz algebras.