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

Published online by Cambridge University Press:  06 March 2017

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 [email protected]
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 [email protected]
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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.

Type
Research Article
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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