Volume 4,  Issue 3 (GI8), 2003

Article 55

ON SOME RESULTS INVOLVING THE CEBYSEV FUNCTIONAL AND ITS GENERALISATIONS

P. CERONE

SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS
VICTORIA UNIVERSITY OF TECHNOLOGY
PO BOX 14428 MCMC 8001,
VICTORIA, AUSTRALIA.
E-Mail: pc@csm.vu.edu.au

Received 15 November, 2002; Accepted 27 May, 2003.
Communicated by: C.P. Niculescu

ABSTRACT.   Recent results involving bounds of the Cebysev functional to include means over different intervals are extended to a measurable space setting. Sharp bounds are obtained for the resulting expressions of the generalised Cebysev functionals where the means are over different measurable sets.
Key words:
Cebysev functional, Grüss inequality, Measurable functions, Lebesgue integral, Perturbed rules.

2000 Mathematics Subject Classification:
Primary 26D15, 26D20; Secondary 26D10.

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Report of the General Inequalities 8 Conference; September 15-21, 2002, Noszvaj, Hungary
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Convolution Inequalities and Applications
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The Hardy-Landau-Littlewood Inequalities with Less Smoothness
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Continuity Properties of Convex-type Set-Valued Maps
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Carleman's Inequality - History, Proofs and Some New Generalizations
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Andersson's Inequality and Best Possible Inequalities
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On Some Results Involving the Cebysev Functional and its Generalisations
P. Cerone

Separation and Disconjugacy
R.C. Brown

New Norm Type Inequalities for Linear Mappings
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An Integral Approximation in Three Variables
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On Some Spectral Results Relating to the Relative Values of Means
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On Zeros of Reciprocal Polynomials of Odd Degree
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Some New Hardy Type Inequalities and their Limiting Inequalities
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Generalizations of the Triangle Inequality
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A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities
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