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## Weighted two-point quadrature formula of semiclosed type for fuctions of bounded variation

Aglić Aljinović, Andrea; Kovač, Sanja; Pečarić, Josip
Weighted two-point quadrature formula of semiclosed type for fuctions of bounded variation // MASSEE International Congress on Mathematics MICOM 2009, Book of Abstracts
Ohrid, Makedonija, 2009. str. 8-9 (predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
Weighted two-point quadrature formula of semiclosed type for fuctions of bounded variation

Autori
Aglić Aljinović, Andrea ; Kovač, Sanja ; Pečarić, Josip

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
MASSEE International Congress on Mathematics MICOM 2009, Book of Abstracts / - , 2009, 8-9

Skup
MICOM 2009

Mjesto i datum
Ohrid, Makedonija, 16-20.09.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi

Sažetak
The weighted Montgomery identity states that $$f\left(x\right)=\int_a^b w\left(t\right)f\left(t\right)dt+\int_a^b P_w\left(x, t\right)f'\left(t\right)dt,$$ where $f:\left[a, b\right]\to \mathbf{; ; R}; ;$ is a differentiable function such that $f'$ is integrable on $\left[a, b\right]$, $w:\left[a, b\right]\to\left[0, \infty\right\rangle$ is some normalized weighted function and $P_w\left(x, t\right)$ is the weighted Peano kernel. We construct an extension of this identity for Riemann-Stieltjes integral and obtain some new inequalities for functions of bounded variation and for functions whose first derivatives belong to $L_p$ spaces. We use these results to obtain bounds of the remainder $E\left(f\right)$ of the weighted two-point quadrature formula of semiclosed type $$\int_a^b w\left(t\right)f\left(t\right)dt=A_1 f\left(a\right)+A_2f\left(x_2\right)+E\left(f\right),$$ where $A_1+A_2=1.$ In particular, we apply all the results with some well-known weighted functions. As special cases, the weighted quadrature formulae of Radau type and related inequalities are obtained.

Izvorni jezik
Engleski

Znanstvena područja
Matematika