OSTROWSKI TYPE INEQUALITIES FOR HARMONICALLY s-CONVEX FUNCTIONS

Year 2015, Volume: 3 Issue: 1, 63 - 74, 01.04.2015

İmdat İşcan

Abstract

The author introduces the concept of harmonically s-convex functions and establishes some Ostrowski type inequalities and a variant of Hermite- Hadamard inequality for these classes of functions.

Keywords

Harmonically s-convex function, Ostrowski type inequality, Hermite- Hadamard's inequality, hypergeometric function

References

• [1] M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
• [2] M. Alomari, M. Darus, S. S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (1) (2010), 1071-1076.
• [3] M. W. Alomari, M. Darus, and U. S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Sci. B31, no.4 (2011), 1643{1652.
• [4] M. Avci, H. Kavurmaci and M. Emin  Ozdemir, New inequalities of Hermite{Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput. 217 (2011) 5171{5176.
• [5] S.S. Dragomir, S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4) (1999), 687{696.
• [6] S. Hussain, M. I. Bhatti, and M. Iqbal, Hadamard-type inequalities for s-convex functions I, J. Math., Punjab Univ. 41 (2009), 51{60.
• [7] H. Hudzik , L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100{111.
• [8] İ. İşcan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math. 86, No.4 (2013), 727-746.
• [9] İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Vol: 43 (6) (2014), 935-942.
• [10] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals, Applicable Analysis, vol. 93, issue 9 (2014), 1846-1862.
• [11] U. S. Kirmaci, M. Klaricic Bakula, M.E.  Ozdemir, and J. Pecaric, Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193, no.1 (2007), 26{35.
• [12] Z. Liu, A note on Ostrowski type inequalities related to some s-convex functions in the second sense, Bull. Korean Math. Soc. 49 (4) (2012), 775-785. Available online at http://dx.doi.org/10.4134/BKMS.2012.49.4.775.
• [13] A. Ostrowski, Uber die Absolutabweichung einer dierentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv. 10 (1938) 226{227.