• 대한수학회지
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• 제38권2호
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• pp.409-420
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• 2001

In this paper we establish a Fubini theorem for various analytic Wiener and Feynman integrals. We then proceed to obtain several integration formulas as corollaries.

• 대한수학회지
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• 제38권2호
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• pp.421-435
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• 2001

In this paper we use a general Fubini theorem established in [13] to obtain several Feynman integration formulas involving analytic Fourier-Feynman transforms. Included in these formulas is a general Parseval's relation.

• 대한수학회보
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• 제50권1호
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• pp.217-231
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• 2013

In this paper we establish a Fubini theorem for generalized analytic Feynman integral and $L_1$ generalized analytic Fourier-Feynman transform for the functional of the form $$F(x)=f({\langle}{\alpha}_1,\;x{\rangle},\;{\cdots},\;{\langle}{{\alpha}_m,\;x{\rangle}),$$ where {${\alpha}_1$, ${\cdots}$, ${\alpha}_m$} is an orthonormal set of functions from $L_{a,b}^2[0,T]$. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.

• 대한수학회보
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• 제40권3호
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• East Asian mathematical journal
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• 제31권1호
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• pp.135-144
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• 2015

In this paper we establish several formulas for multiple integral transform of functionals defined on abstract Wiener space. We then use the these results to establish several basic formulas involving multiple convolution products.

• 호남수학학술지
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• 제44권2호
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• pp.271-280
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• 2022

In this study, We have applied the right operator k-Riemann-Liouville is involving two orders α and β with a positive parameter p > 0, further, the left operator k-Riemann-Liouville is used with the negative parameter p < 0 to introduce a new version related to Hardy-type inequalities. These inequalities are given and reversed for the cases 0 < p < 1 and p < 0. We then improved and generalized various consequences in the framework of Hardy-type fractional integral inequalities.