• 대한수학회지
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• 제59권3호
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• pp.469-494
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• 2022

In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.907-921
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• 2023

In this article, we are presenting and examining a subclass of Meromorphic univalent functions as stated by the Bessel function. We get disparities in terms of coefficients, properties of distortion, closure theorems, Hadamard product. Finally, for the class Σ^*(℘, ℓ, ℏ, τ, c), we obtain integral transformations.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.937-946
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• 2023

In this present work, we inaugurated subclasses of analytic functions which are associated with generalized Mittag Leffler Functions. Inclusion implications and integral preserving properties under the Bernardi integral operator are investigated. Some consequences of these findings are also illustrated.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.31-46
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• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.167-178
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• 2016

In this paper, we study the stochastic integral of processes taking values of generalized operators based on a triple E ⊂ H ⊂ E^∗, where H is a Hilbert space, E is a countable Hilbert space and E^∗ is the strong dual space of E. For our purpose, we study E-valued Wiener processes and then introduce the stochastic integral of L(E, F^∗)-valued process with respect to an E-valued Wiener process, where F^∗ is the strong dual space of another countable Hilbert space F.

• 한국인터넷방송통신학회논문지
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• 제9권1호
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• pp.31-37
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• 2009

본 논문은 컬러영상의 특정 클러스터에 해당하는 낙관을 추출하기 위하여 확장된 퍼지적분을 제안하였다. 기존의 퍼지적분은 평가항목에 대한 부정적인 측면을 강조하였다. 제안된 방법은 무게중심법을 통하여 인접정보를 이용하여 평가항목간의 보상적인 측면을 고려하였다. 평가 항목간의 min 연산자로서의 기존의 퍼지적분의 특징에만 기초하는 방법은 낙관 영상의 끊어지는 부분 처리와 전체적인 영상의 유연성을 확보하는 데는 다소 부족한 느낌이 들었다. 그래서 이를 해결하기 위해 무게중심을 이용하여 전체적인 영상의 유연성을 확보 하였다. 그 결과 실 생활의 영수증의 낙관을 분리하는 실질적인 문제에 관한 자료들에 대하여 실험을 수행하였다.

• 한국통신학회논문지
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• 제29권6C호
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• pp.815-823
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• 2004

색상(hue) 기반 주목연산자와 조합누적투영함수(combinational integral projection function: CIPF)를 제안하여 조명변화에 강건하게 정규화된 얼굴요소영역을 추출하였다. 살색 필터를 도입하여 얼굴후보영역들을 추출하고, 거기에 색상과 대칭성에 기반한 주목연산자를 적용하여 조명변화에 강건하게 두 눈의 위치를 정확히 검출할 수 있도록 하였으며, 색상기반 눈 분산 필터로 눈을 검증하여 얼굴영역을 확인하였다. 또한, 색상과 밝기 성분을 조합한 조합누적투영함수를 사용하여 두 눈의 위치를 기준으로 조명변화나 수염의 존재유무에 둔감하게 눈썹 및 입의 수직위치를 구하고, 이를 바탕으로 정규화된 얼굴영역 및 그 요소영역을 추출하였다. AR 얼굴 데이터베이스［8］에 제안한 색상기반 주목연산자를 적용한 결과 기존 명도기반 주목연산자에 비해 약 39.3%의 눈 검출 성능향상을 보임으로써 조명방향 변화에 강건하게 정규화된 얼굴 및 그 요소영역을 일관성 있게 추출할 수 있음을 확인하였다.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.433-448
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• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

• 충청수학회지
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• 제5권1호
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• pp.159-165
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• 1992

In 1986, R. Huff [3] showed that a Dunford integrable function is Pettis integrable if and only if T : $X^*{\rightarrow}L_1(\mu)$ is weakly compact operator and {$T(K(F,\varepsilon))|F{\subset}X$, F : finite and ${\varepsilon}$ > 0} = {0}. In this paper, we introduce the notion of Bourgain property of real valued functions formulated by J. Bourgain [2]. We show that the class of pettis integrable functions is linear space and if lis bounded function with Bourgain property, then T : $X^{**}{\rightarrow}L_1(\mu)$ by $T(x^{**})=x^{**}f$ is $weak^*$ - to - weak linear operator. Also, if operator T : $L_1(\mu){\rightarrow}X^*$ with Bourgain property, then we show that f is Pettis representable.