Integral Inequalities of the Ostrowski Type

Volume 3, Issue 2, 2002

Article 21

INTEGRAL INEQUALITIES OF THE OSTROWSKI TYPE

SCHOOL OF COMMUNICATIONS AND INFORMATICS
VICTORIA UNIVERSITY OF TECHNOLOGY
PO BOX 14428
MELBOURNE CITY MC
VICTORIA 8001, AUSTRALIA.
E-Mail: sofo@matilda.vu.edu.au

Received December, 2000; Accepted 16 November, 2001.
Communicated by: T. Mills

ABSTRACT. Integral inequalities of Ostrowski type are developed for n-times differentiable mappings, with multiple branches, on the L_¥ norm. Some particular inequalities are also investigated, which include explicit bounds for perturbed trapezoid, midpoint, Simpson's, Newton-Cotes and left and right rectangle rules. The results obtained provide sharper bounds than those obtained by Dragomir [5] and Cerone, Dragomir and Roumeliotis [2].

[2] P. CERONE, S.S. DRAGOMIR and J. ROUMELIOTIS, An
inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, East Asian J. of Math., 15(1) (1999), 1-9.
[5] S.S. DRAGOMIR, A generalization of Ostrowski's integral inequality for mappings whose derivatives belong to L_¥[a, b] and applications in numerical integration, SUT. J. of Math., (in press)

Key words:
Ostrowski Integral Inequality, Quadrature Formulae.

2000 Mathematics Subject Classification:
26D15, 41A55.

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