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BOUNDS FOR THE DEVIATION OF A FUNCTION FROM THE CHORD GENERATED BY ITS EXTREMITIES

Part of: Inequalities

Published online by Cambridge University Press:  01 October 2008

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
School of Computer Science and Mathematics, Victoria University, PO Box 14428, Melbourne City Mail Centre, Vic, 8001, Australia (email: [email protected])
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Abstract

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Sharp bounds for the deviation of a real-valued function f defined on a compact interval [a,b] to the chord generated by its end points (a,f(a)) and (b,f(b)) under various assumptions for f and f′, including absolute continuity, convexity, bounded variation, and monotonicity, are given. Some applications for weighted means and f-divergence measures in information theory are also provided.

Keywords

bounded variationabsolute continuityconvexitymonotonicityweighted meansanalytic inequalitiesf-divergence measuresinformation theory

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 225 - 248
Copyright
Copyright © 2008 Australian Mathematical Society

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