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EXTENSIONS OF THE HERMITE–HADAMARD INEQUALITY FOR $r$-PREINVEX FUNCTIONS ON AN INVEX SET

Part of: Inequalities

Published online by Cambridge University Press:  06 March 2017

DAH-YAN HWANG  and
SILVESTRU SEVER DRAGOMIR
DAH-YAN HWANG*
Affiliation:
Department of Information and Management, Taipei City University of Science and Technology, No. 2, Xueyuan Road, Beitou, 112, Taipei, Taiwan email dyhuang@tpcu.edu.tw
SILVESTRU SEVER DRAGOMIR
Affiliation:
Mathematics, 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, Johannesburg 2050, South Africa email sever.dragomir@vu.edu.au
*
✉dyhuang@tpcu.edu.tw
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Abstract

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Necessary and sufficient conditions to characterise weakly $r$-preinvex functions on an invex set are obtained and used to establish generalisations of the Hermite–Hadamard inequality for such functions.

Keywords

extended meansinvex setr-convexr-preinvexHermite–Hadamard inequality

MSC classification

Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 90C25: Convex programming
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 412 - 423
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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