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REFINING RECURSIVELY THE HERMITE–HADAMARD INEQUALITY ON A SIMPLEX

Part of: Functions of several variables

Published online by Cambridge University Press:  17 April 2015

MUSTAPHA RAÏSSOULI  and
SEVER S. DRAGOMIR
MUSTAPHA RAÏSSOULI*
Affiliation:
Department of Mathematics, Faculty of Science, Taibah University, Al Madinah Al Munawwarah, PO Box 30097, 41477, Kingdom of Saudi Arabia Department of Mathematics, Faculty of Science, Moulay Ismail University, Meknes, Morocco email raissouli.mustapha@gmail.com
SEVER S. DRAGOMIR
Affiliation:
Research Group in Mathematical Inequalities and Applications, School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa email sever.dragomir@vu.edu.au
*
✉raissouli˙10@hotmail.com
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Abstract

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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.

Keywords

convexitysimplexHermite–Hadamard inequalityrefinementconvergence of recursive algorithms

MSC classification

Primary: 26B25: Convexity, generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 57 - 67
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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