• 대한수학회논문집
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• 제13권2호
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• pp.307-316
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• 1998

In this paper Denjoy*-Dunford, Denjoy*-Pettis, Denjoy*-McShane and Denjoy*-Bochner integrals of functions which map an interval [a,b] into a Banach space X are defined. And we give the relations among the integrals.

• 대한수학회논문집
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• 제32권4호
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• pp.979-990
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• 2017

Inspired by the results obtained by Brychkov ([2]), the authors evaluate a large number of new and interesting double definite integrals. The results are obtained with the use of classical hypergeometric summation theorems and a well-known double finite integral due to Edwards ([3]). The results are given in terms of Psi and Hurwitz zeta functions suitable for numerical computations.

• 대한수학회지
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• 제40권2호
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• pp.251-272
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• 2003

Multidimensional integrals are expressed in terms of lower dimensional integrals and function evaluations. An iterative process is used where a trapezoidal and three point identities are used as generators for higher dimensional identities. Bounds are obtained utilising the resulting identities. It is demonstrated that earlier Ostrowski type results are obtained as particular instances of the current work.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.9-13
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• 2003

In this paper, we will define comonotonically additive interval-valued functionals which are generalized comonotonically additive real-valued functionals in Shcmeildler[14] and Narukawa[12], and study some properties of them. And we also investigate some relations between comonotonically additive interval-valued functionals and interval-valued Choquet integrals on a suitable function space cf.[19,10,11,13].

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.127-128
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• 2008

In this paper, we consider define fuzzy invex sets and fuzzy preinvex functions on the class of Choquet integrable functions, and interval-valued fuzzy invex sets and interval-valued fuzzy preinvex functions on the class of interval-valued Choquet integrals. And also we prove some properties of them.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.131-132
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• 2008

In this paper, we consider interval probability as a unifying concept for uncertainty and Choquet integrals with resect to a capacity functional. By using interval probability, we will define an interval-valued capacity functional and Choquet integrals with respect to an interval-valued capacity functional. Furthermore, we investigate Choquet Choquet weak convergence of interval-valued capacity functionals of random sets.

• 충청수학회지
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• 제21권2호
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• 충청수학회지
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• 제26권1호
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• pp.111-123
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• 2013

Cameron and Storvick discovered change of scale formulas for Wiener integrals on classical Wiener space. Yoo and Skoug extended this result to an abstract Wiener space. In this paper, we investigate a change of scale formula for generalized Wiener integrals of various functions using the generalized Fourier-Feynman transform.

• 대한수학회지
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• 제43권3호
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• pp.563-578
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• 2006

The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.113-117
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• 2011

In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect to a fuzzy measure of real-valued measurable functions. In doing so, we investigate some basic properties and convergence theorems.