Hermite-Hadamard type inequalities for logarithmically B-preinvex functions

Volume 9, Issue 12, pp 6096--6112 http://dx.doi.org/10.22436/jnsa.009.12.16

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Authors

Fiza Zafar - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Nusrat Yasmin - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. Hina Mehboob - Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan.

Abstract

In this paper, we introduce the notion of logarithmically B-preinvex functions and establish certain new Hermite-Hadamard type inequalities for the functions whose derivatives in absolute value are logarithmically B-preinvex. Our results generalize several known results for the classes of logarithmically preinvex functions. Some estimates for the left and right hand side of the Hermite-Hadamard inequality are also obtained for a new class of differentiable logarithmically \(\alpha\)-preinvex functions.

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Keywords

• Hermite-Hadamard inequality
• logarithmically B-preinvex functions
• convex functions.

MSC

•  26A51
•  26D15
•  26B25
•  52A30

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