• 충청수학회지
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• 제23권2호
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• pp.207-213
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• 2010

In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.363-379
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• 2022

In this paper, we carried out a new numerical approach for solving integral algebraic equations with weakly singular kernels. The novel method is based on the construction of B-spline tight framelets using the unitary and oblique extension principles. Some numerical examples are given to provide further explanation and validation of our method. The result of this study introduces a new technique for solving weakly singular integral algebraic equation and thus in turn will contribute to providing new insight into approximation solutions for integral algebraic equation (IAE).

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.13-21
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• 2019

In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.

• 대한수학회보
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• 제33권3호
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• pp.411-417
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• 1996

Some generalizations of the Riemann integral have been studied for real-valued functions. One of these generalizations leads to an integral, often called the McShane integral, that is equivalent to the Lebesgue integral.

• 충청수학회지
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• 제19권2호
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• pp.177-188
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• 2006

In this paper, we define and study the vector-valued ap-Henstock-Stieltjes integral, we prove the Cauchy extension theorem and the dominated convergence theorems for the ap-Henstock-Stieltjes integral.

• 대한수학회보
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• 제43권1호
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• pp.77-80
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• 2006

Let K be a number field, $K_n$ its ray class field with conductor n and L a Galois extension of K containing $K_n$. We prove that $L/K_n$ has a relative integral basis (RIB) under certain simple condition. Also we reduce the problem of the existence of a RIB to a quadratic extension of $K_n$ under some condition.

• 대한수학회논문집
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• 제36권2호
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• pp.277-298
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• 2021

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

• 대한수학회논문집
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• 제22권1호
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• pp.27-39
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• 2007

In this paper, we define and study the C-integral of functions mapping an interval [a,b] into a Banach space X and discuss the relations among Henstock integral, C-integral and McShane integral. We also study the Denjoy extension of the C-integral.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.123-130
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• 2002

In this paper we introduce the concepts of Denjoy-Stieltjes-Dunford, Denjoy-Stieltjes-Pettis and Denjoy-Stieltjes-Bochner integrals of Banach-valued functions and then prove some properties of them.

• 충청수학회지
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• 제31권1호
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• pp.151-160
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• 2018

In this paper we introduce the AP-Henstock-Stieltjes integral for fuzzy-number-valued functions which is an extension of the Henstock-Stieltjes integral and investigate some properties.