Skip to content
Open Access Published by De Gruyter Open Access March 7, 2014

Some Ostrowski’S Type Inequalities For Functions Whose Second Derivatives Are S-Convex In The Second Sense

  • Erhan Set EMAIL logo , Mehmet Zeki Sarikaya, EMAIL logo and M. Emin Ozdemir EMAIL logo
From the journal Demonstratio Mathematica

Abstract

Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given

References

[1] M. Alomari, M. Darus, Some Ostrowski’s type inequalities for convex functions with applications, RGMIA 13(1) (2010), Article 3. [ONLINE: http://ajmaa.org/RGMIA/v13n1.php]Search in Google Scholar

[2] M. Alomari, M. Darus, S. S. Dragomir, P. Cerone, Ostrowski’s inequalities for functions whose derivatives are s-convex in the second sense, RGMIA 12 (2009), Supp., No. 15.Search in Google Scholar

[3] P. Cerone, S. S. Dragomir J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll. 1(1) (1998), Article 4.Search in Google Scholar

[4] S. S. Dragomir, S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl.Math. Lett. 11 (1998), 105-109.10.1016/S0893-9659(97)00142-0Search in Google Scholar

[5] M. Z. Sarıkaya, On the Ostrowski type integral inequality, Acta Math. Univ. Comenianae 79(1) (2010), 129-134.Search in Google Scholar

[6] E. Set, M. E. Özdemir, M. Z. Sarıkaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Unv. Ser. Math. Inform. 27(1) (2012), 67-82.Search in Google Scholar

[7] M. E. Özdemir, H. Kavurmaci, E. Set, Ostrowski’s type inequalities for p ;mq-convex functions, Kyungpook Math. J. 50 (2010), 371-378.10.5666/KMJ.2010.50.3.371Search in Google Scholar

[8] M. Z. Sarıkaya, E. Set, M. E. Özdemir, On the integral inequalities for mappings whose second dervatives are convex and applications, Stud. Univ. Babes-Bolyai Math., in press.Search in Google Scholar

[9] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13-20.Search in Google Scholar

[10] S. S. Dragomir, S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32(4) (1999), 687-696.10.1515/dema-1999-0403Search in Google Scholar

[11] H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1994), 100-111.10.1007/BF01837981Search in Google Scholar

[12] A. Ostrowski,Über die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv. 10 (1938), 226-227.10.1007/BF01214290Search in Google Scholar

Published Online: 2014-03-07
Published in Print: 2014-03-1

This content is open access.

Downloaded on 19.3.2024 from https://www.degruyter.com/document/doi/10.2478/dema-2014-0003/html
Scroll to top button