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Bull. Korean Math. Soc. 2012; 49(4): 775-785

Printed July 1, 2012

https://doi.org/10.4134/BKMS.2012.49.4.775

Copyright © The Korean Mathematical Society.

A note on Ostrowski type inequalities related to some $s$-convex functions in the second sense

Zheng Liu

University of Science and Technology Liaoning

Abstract

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Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are $s$-convex in the second sense is established. Special cases are discussed.

Keywords: Ostrowski type inequality, convex function, $s$-convex function, H\"older inequality, averaged midpoint-trapezoid inequality

MSC numbers: 26D15

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