IJPAM: Volume 26, No. 3 (2006)

IYENGAR TYPE ESTIMATE OF ERROR
IN TRAPEZOIDAL RULE

I. Franjic$^1$, J. Pecaric$^2$, I. Peric$^3$
$^{1,3}$Department of Mathematics
Faculty of Food Technology and Biotechnology
University of Zagreb
Pierottijeva 6, Zagreb, 10000, CROATIA
$^1$e-mail: ifranjic@pbf.hr
$^3$e-mail: iperic@pbf.hr
$^2$Faculty of Textile Technology
University of Zagreb
Pierottijeva 6, Zagreb, 10000, CROATIA
e-mail: pecaric@hazu.hr


Abstract.Using Hayashi's inequality, weighted Iyengar type inequality for functions with bounded higher derivatives is derived. This result generalizes results obtained by P. Cerone in [#!Cerone!#] and H. Gauchman in [#!G!#]. It also improves estimation obtained by Feng Qi in [#!Qi!#].

Received: May 2, 2005

AMS Subject Classification: 26D10, 26D15

Key Words and Phrases: Iyengar's inequality, Steffensen's inequality, trapezoidal rule, bounded higher derivatives

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 3