SOME NEW RESULTS ON THE FEJÉR AND HERMITE-HADAMARD INEQUALITIES

The Hermite-Hadamard inequality and its generalization, the Fejér inequality, have many applications. A simple application is to approximate the definite integral $\int_a^b {f\left( x \right)} \,dx$if the function f is convex. In this short note, we show how to relax the convexity property of the fu...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2013-01, Vol.43 (5), p.1625-1636
Main Authors: HUY, VU NHAT, NGÔ, QUÕC-ANH
Format: Article
Language:English
Subjects:
Fejér
Hermite-Hadamard
Integral inequality
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Summary:The Hermite-Hadamard inequality and its generalization, the Fejér inequality, have many applications. A simple application is to approximate the definite integral $\int_a^b {f\left( x \right)} \,dx$if the function f is convex. In this short note, we show how to relax the convexity property of the function f, and thus we obtain inequalities that involve a larger class of functions. This new study also raises some open questions.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2013-43-5-1625