Volume 3,  Issue 2, 2002

Article 21

INTEGRAL INEQUALITIES OF THE OSTROWSKI TYPE

A. SOFO

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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Other papers in this issue

An Error Estimate for Finite Volume Methods for the Stokes Equations
A. Alami-Idrissi and M. Atounti 

On Some Retarded Integral Inequalities and Applications 
B.G. Pachpatte 

Littlewood's Inequality for p-Bimeasures
Nasser Towghi

Monotonicity Properties of the Relative Error of a Padé Approximation for Mills' Ratio
Iosif Pinelis 

Integral Inequalities of the Ostrowski Type
A.Sofo

Multidimensional Extension of L.C. Young's Inequality
Nasser Towghi 

Inequalities for Lattice Constrained Planar Convex Sets
 Poh Wah Hillock and Paul R. Scott 

Some Results Concerning Best Uniform Coapproximation
Geetha S. Rao and R. Saravanan

Strongly Elliptic Operators for a Plane Wave Diffraction Problem in Bessel Potential Spaces
L.P. Castro

Some Integral Inequalities Involving Taylor's Remainder. I
Hillel Gauchman

On Multidimensional Grüss Type Inequalities
Baburao G. Pachpatte

Two Remarks on the Stability of Generalized Hemivariational Inequalities
 Mohamed Ait Mansour 

Note on the Perturbed Trapezoid Inequality
 Xiao-liang Cheng and Jie Sun

On a Noncoercive System of Quasi-Variational Inequalities Related to Stochastic Control Problems
M. Boulbrachene, M. Haiour and B. Chentouf

An Inequality Improving the First Hermite-Hadamard Inequality for Convex Functions Defined on Linear Spaces and Applications for Semi-Inner Products
 S.S. Dragomir

 

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