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An Approximation of the Hankel Transform for Absolutely Continuous Mappings
DRAGOMIR, N.M.,DRAGOMIR, S.S.,GU, M.,GAN, X.,WHITE, R. 한국산업정보응용수학회 2002 한국산업정보응용수학회 Vol.6 No.1
Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel's transform of absolutely continuous mapping.
A QUADRATURE RULE FOR THE FINITE HILBERT TRANSFORM VIA TRAPEZOID TYPE INEQUALITIES
Dragomir, N.M.,Dragomir, S.S.,Farrell, P.M.,Baxter, G.W. 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
A quadrature rule for the finite Hilbert Trasnform via trapezoid type inequalities is obtained . Some numerical experiments for different divisions of the interval [a, b] are also presented.
Dragomir, Sever Silvestru Korean Mathematical Society 2007 대한수학회보 Vol.44 No.3
Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.
SOME DISCRETE INEQUALITIES OF GRÜSS TYPE AND APPLICATIONS IN GUESSING THEORY
DRAGOMIR, S.S. The Honam Mathematical Society 1999 호남수학학술지 Vol.21 No.1
Some discrete inequalities of $Gr{\ddot{u}}ss$ type and their applications in estimating the p-moments of guessing mapping are given.
NEW ESTIMATES OF THE CEBYSEV FUNCTIONAL FOR STIELTJES INTEGRALS AND APPLICATIONS
Dragomir, S.S. Korean Mathematical Society 2004 대한수학회지 Vol.41 No.2
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.
INEQUALITIES FOR THE RIEMANN-STIELTJES INTEGRAL OF PRODUCT INTEGRATORS WITH APPLICATIONS
Dragomir, Silvestru Sever Korean Mathematical Society 2014 대한수학회지 Vol.51 No.4
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.