• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.75-92
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• 2004

A generalised integration by parts formula for sequences of absolutely continuous functions that satisfy the ${\omega}-Appell$ condition and different estimates for the remainder are provided. Applications for particular instances of such sequences are pointed out as well.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.23-28
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• 1997

In this paper, we investigate continuity of $$F(x)=(H){\int}_a^x\;fdG$$ and Henstock-Stieltjes integrability of product of two functions and obtain the formula of integration by parts for the Henstock-Stieltjes integral.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.89-94
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• 2020

In this paper we introduce the concept of the AP-Henstock integral and prove the integration by parts formula for the AP-Henstock integral.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1093-1103
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• 2022

In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces (H, B, 𝜈). To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in 𝓛(B), the Banach space of bounded linear operators from B to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in 𝓛(B). We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.485-501
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• 2001

In this paper we express analytic Feynman integral of the first variation of a functional F in terms of analytic Feynman integral of the product F with a linear factor and obtain an integration by parts formula of the analytic Feynman integral of functionals on abstract Wiener space. We find the Fourier-Feynman transform for the product of functionals in the Fresnel class F(B) with n linear factors.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.57-69
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• 2014

We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.553-564
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• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.607-613
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• 2009

In this paper, we define the C-integral and prove the integration by parts formula for the C-integral.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.861-870
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• 2010

In this paper, we define the $M_{\alpha}$-integral and prove the integration by parts formula for the $M_{\alpha}$-integral.