• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.437-468
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• 2001

This paper is an exposition of the relationship between Witten's functional integral and Vassiliev invariants.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.49-59
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• 2001

In this paper we introduce the modified conditional Yeh-Wiener integral. To do so, we first treat the modified Yeh-Wiener integral. And then we obtain the simple formula for the modified conditional Yeh-Wiener integral and valuate the modified conditional Yeh-Wiener integral for certain functional using the simple formula obtained. Here we consider the functional using the simple formula obtained. Here we consider the functional on a set of continuous functions which are defined on various regions, for example, triangular, parabolic and circular regions.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.395-398
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• 2006

In this note, for any given positive integer n, we determine all the continuous solutions f : R ${\rightarrow}$ R of the integral-functional equation $f^n(x)=n_{_o}{^x}f(t)dt$.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.155-166
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• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.87-102
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• 2012

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional $[{\Delta}^kF]^{\^}$. We conclude by applying our series expansion to several interesting functionals.

• East Asian mathematical journal
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• v.23 no.2
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• pp.229-246
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• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.295-308
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• 2004

In this paper, we prove the existence of integral solutions, defined on a compact interval, for functional differential inclusion with nonlocal conditions and impulsive functional differential inclusions in a Banach space.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1161-1168
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• 2016

Belarbi and Dahmani [3], recently, using the Riemann-Liouville fractional integral, presented some interesting integral inequalities for the Chebyshev functional in the case of two synchronous functions. Subsequently, Dahmani et al. [5] and Sulaiman [17], provided some fractional integral inequalities. Here, motivated essentially by Belarbi and Dahmani's work [3], we aim at establishing certain (presumably) new inequalities associated with pathway fractional integral operators by using synchronous functions which are involved in the Chebychev functional. Relevant connections of the results presented here with those involving Riemann-Liouville fractional integrals are also pointed out.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.57-79
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• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.249-264
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• 2004

In this paper, some new estimates of the Cebysev functional for Stieltjes integrals are provided. Applications for quadrature formulae in approximating the Riemann-Stieltjes integral are also given.