New Ostrowski Type Inequalities for Trigonometrically Convex Functions Via Classical Integrals-Reference-Cited by-同舟云学术

New Ostrowski Type Inequalities for Trigonometrically Convex Functions Via Classical Integrals

Published:2022-08-23 Issue: Volume: Page:
ISSN:2147-1762
Container-title:GAZI UNIVERSITY JOURNAL OF SCIENCE
language:en
Short-container-title:

Author:

DEMİR Şenol¹,MADEN Selahattin²

Affiliation:

1. KARADENİZ TEKNİK ÜNİVERSİTESİ

2. ORDU UNIVERSITY

Abstract

In the paper, we introduce the class of trigonometrically convex functions and using the Hölder, Hölder-İşcan, Power-mean and Improved power-mean integral inequality together with an identity we establish some new inequalities of Ostrowski-type for functions whose second derivatives are trigonometrically convex which is a special case of h-convex functions. Some applications for special means are also given.

Publisher

Gazi University Journal of Science

Subject

Multidisciplinary,General Engineering

Reference17 articles.

1. Ostrowski, A., “Über Die Absolutabweichung einer differentiierbaren funktion von ihrem integralmittelwert”, Comment. Math. Helv., 10(1): 226–227, (1937).

2. Alomari, M., Darus, M., Dragomir, S.S., Cerone, P., “Ostrowski’s Inequalities for Functions Whose Derivatives are s-Convex in the Second Sense”, RGMIA Res. Rep. Coll. 12, Supplement, Article 15, (2009).

3. Barnett, N.S., Cerone, P., Dragomir, S.S, Pinheiro, M.R., Sofo, A., “Ostrowski Type Inequalities for Functions Whose Modulus of Derivatives are Convex and Applications”, RGMIA Res. Rep. Coll. 5 (2): Article 1, (2002).

4. Cerone, P., Dragomir, S.S., Roumeliotis, J., “An Inequality Of Ostrowski Type for Mappings Whose Second Derivatives are Bounded and Applications”, RGMIA Res. Rep. Coll. 1 (1): Article 4(1998).

5. Dragomir, S.S., “Some Companions of Ostrowski’s Inequality for Absolutely Continuous Functions and Applications”, Bull. Korean Math. Soc., 42(2): 213–230, (2005).