• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.471-480
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• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• 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 ${\int}_0^T{\theta}(t)\;dy(t)$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.187-193
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• 2010

In this paper, the moments of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs(RNT) distribution over a general interval [a, b] $\subset$ [0, 1], are found through the moments of the RNT distribution over the unit interval, [0, 1]. This is done using some special features of the distribution and the fact that [0, 1] is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval.