Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2017; 32(3): 601-617

Online first article July 12, 2017      Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160145

Copyright © The Korean Mathematical Society.

Certain generalized Ostrowski type inequalities for local fractional integrals

Junesang Choi, Erhan Set, and Muharrem Tomar

Dongguk University, Ordu University, Ordu University

Abstract

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We give a function associated with generalized Ostrowski type inequality and its integral representation for local fractional calculus. Then, using this function and its integral representation, we establish several inequalities of generalized Ostrowski type for twice local fractional differentiable functions. We also consider some special cases of the main results which are further applied to a concrete function to yield two interesting inequalities associated with two generalized means.

Keywords: local fractional calculus, Hermite-Hadamard inequality, generalized convex functions, H\"{o}lder's inequality, generalized Ostrowski inequality

MSC numbers: 26A33, 26A51, 26D07, 26D10, 26D15

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