• Korean Journal of Mathematics
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• 제11권2호
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• pp.137-146
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• 2003

In this paper we introduce the concepts of the weak $Denjoy_*$ integral of real-valued functions and the weak $Denjoy_*$-Dunford, weak $Denjoy_*$-Pettis, weak $Denjoy_*$-Bochner, weak $Denjoy_*$-McShane integrals of Banach-valued functions and then investigate some of their properties.

• 대한수학회보
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• 제56권6호
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• pp.1423-1433
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• 2019

Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.

• 대한수학회보
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• 제54권6호
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• pp.1951-1967
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• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.315-327
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• 2008

In this paper we introduce the concepts of $Denjoy_*$-Stieltjes-Dunford, $Denjoy_*$-Stieltjes-Pettis, $Denjoy_*$-Stieltjes-Bochner and $Denjoy_*$-McShane-Stieltjes integrals of Banach-valued functions using the $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.297-306
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• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• 충청수학회지
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• 제8권1호
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• pp.119-130
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• 1995

I study the extension of the definition of the analytic operator-valued Feynman integral to potentials given by a class of signed measures described in terms of additive functionals associated with regular Dirichlet forms.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.455-465
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• 2022

We point out a flaw in a result proved by Singh and Shah [Kyungpook Math. J., 57(2017), 537-543] which was recently published in Kyungpook Mathematical Journal. Further, we point out an error in another result of the same paper which we correct and obtain integral extension of the corrected form.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.281-288
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• 2010

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

• 충청수학회지
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• 제23권4호
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• pp.879-884
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• 2010

In this paper, we introduce the AP-Henstock Dunford, AP-Henstock Pettis and AP-Henstock Bochner integral Banach-valued functions and investigate some properties of the these integrals.

• 대한기계학회논문집A
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• 제33권9호
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• pp.930-937
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• 2009

The estimation method of the fracture resistance curve for the pipe specimen was proposed using the load ratio method for the standard specimen. For this, the calculation method of the load - CMOD curve for the pipe specimen with the common format equation(CFE) was proposed by using data of the CT specimen. The proposed method agreed well with experimental data. The J-integral value and the crack extension were calculated from the estimated load - CMOD data. The fracture resistance curve was estimated from the calculated J-integral and the crack extension. From these results, it have been seen that the proposed method is reliable to estimate the J-R curve of the pipe specimen.