• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.791-815
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• 2014

We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.181-199
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• 2016

In this paper we obtain some retarded integral inequalities involving Stieltjes derivatives and we use our results in the study of various qualitative properties of a certain retarded impulsive differential equation.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.137-143
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• 2000

In this paper, we define the uniformly sequence for the vector valued McShand-Stieltjes integrable functions and prove the dominated convergence theorem for the McShand-Stieltjes integrable functions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.555-558
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• 2003

The Choquet-Stieltjes integral is defined. It is shown that the Choquet -Stieltjes integral is rep-resented by a Choquet integral. As an application of the theorem above, it is shown that Choquet expected utility model for decision under uncertainty and rank dependent utility model for decision under .risk are respectively same as their simplified version.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.1-19
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• 2017

In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.

• 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.5 no.2
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• pp.65-73
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• 1990

• The Mathematical Education
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• v.22 no.1
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• pp.53-56
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• 1983

• 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 ${\int}_0^T{\theta}(t)\;dy(t)$.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.227-231
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• 2008

We give some relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation 1 - a = $a^m$ over different intervals, which generalizes recent results([6]) for a = ${\frac{1}{2}}$.