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REFINING RECURSIVELY THE HERMITE–HADAMARD INEQUALITY ON A SIMPLEX
Part of
- Functions of several variables
MUSTAPHA RAÏSSOULI, SEVER S. DRAGOMIR
Journal:

Bulletin of the Australian Mathematical Society / Volume 92 / Issue 1 / August 2015

Published online by Cambridge University Press:

17 April 2015, pp. 57-67

Print publication:

August 2015
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In the present paper, a coupled algorithm refining recursively the Hermite–Hadamard inequality on a simplex is investigated. Our approach allows us to express the integral mean value $M_{f}$ of a convex function $f$ on a simplex as both the limit of sequences and sum of series involving iterative lower and upper bounds of $M_{f}$. Two examples of interest are discussed.