Certain Ostrowski type inequalities for generalized \(s\)-convex functions

Volume 10, Issue 11, pp 5947--5957 http://dx.doi.org/10.22436/jnsa.010.11.32

Publication Date: November 24, 2017 Submission Date: June 06, 2017

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Authors

Muharrem Tomar - Department of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200 Ordu, Turkey. Praveen Agarwal - Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India. - Department of Mathematics, Ahi Evran University, 40100 Kırsehir, Turkey. Mohamed Jleli - Department of Mathematics, King Saud University, Riyadh-11451, Saudi Arabia. Bessem Samet - Department of Mathematics, King Saud University, Riyadh-11451, Saudi Arabia.

Abstract

In this paper, we first obtain a generalized integral identity for twice local differentiable functions. Then, using functions whose second derivatives in absolute value at certain powers are generalized \(s\)-convex in the second sense, we obtain some new Ostrowski type inequalities.

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Keywords

• Generalized \(s\)-convex functions
• generalized Hermite-Hadamard inequality
• generalized Hölder inequality

MSC

•  26A51
•  26A33
•  26D10

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