Turkish Journal of Analysis and Number Theory
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Turkish Journal of Analysis and Number Theory. 2014, 2(4), 113-118
DOI: 10.12691/tjant-2-4-2
Open AccessArticle

On Some Inequalities for Functions Whose Second Derivatives Absolute Values Are S-Geometrically Convex

MEVLÜT TUNÇ1, , IBRAHİM KARABAYIR2 and EBRU YÜKSEL3

1Mustafa Kemal University, Faculty of Science and Arts, Department of Mathematics, Hatay, Turkey

2The Institute for Graduate Studies in Sciences and Engineering, Kilis 7 Aralk University, Kilis, Turkey

3AGRI Ibrahim Çeçen University, Faculty of Science and Arts, Department of Mathematics, AGRI, Turkey

Pub. Date: July 20, 2014

Cite this paper:
MEVLÜT TUNÇ, IBRAHİM KARABAYIR and EBRU YÜKSEL. On Some Inequalities for Functions Whose Second Derivatives Absolute Values Are S-Geometrically Convex. Turkish Journal of Analysis and Number Theory. 2014; 2(4):113-118. doi: 10.12691/tjant-2-4-2

Abstract

In this paper, the authors achieve some new Hadamard type in- equalities using elementary well known inequalities for functions whose second derivatives absolute values are s-geometrically and geometrically convex. And also they get some applications for special means for positive numbers.

Keywords:
s-geometrically convex geometrically convex Hadamard.s inequality Hölder.s inequality power mean inequality means

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References:

[1]  M. Alomari, M. Darus, S. S. Dragomir: New inequalities of Hermite-Hadamard type for func-tions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., Vol. 41 No. 4 (2010/12), 353-359.
 
[2]  S.S. Dragomir, R.P. Agarwal: Two inequalities for differentiable mappings and applicationsto special means of real numbers and to trapezoidal formula. Appl Math Lett, Vol. 11 No: 5, (1998) 91.95.
 
[3]  Hermite-Hadamard in-equalities and applications, RGMIA monographs, Victoria University, 2000. [Online: http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
 
[4]  J. Hadamard: Étude sur les propriétés des fonctions entières et en particulier d.une function considerée par Riemann, J. Math Pures Appl., 58, (1893) 171. 215.
 
[5]  H. Hudzik and L. Maligranda: Some remarks on s-convex functions, Aequationes Math., Vol. 48 (1994), 100-111.
 
[6]  İ. İscan, Some New Hermite-Hadamard Type Inequalities for Geometrically Convex Functions, Mathematics and Statistics, 1 (2): 86-91, 2013.
 
[7]  İ. İscan, On Some New Hermite-Hadamard type inequalities for s-geometrically convex functions, International Journal of Mathematics and Mathematical Sciences, Volume 2014 (2014), Article ID 163901, 8 pages.
 
[8]  D. S. Mitrinovi´c, J. Peµcari´c and A. M. Fink: Classical and new inequalities in analysis, Kluwer Academic, Dordrecht, 1993.
 
[9]  J. E. Peµcari´c, F. Proschan and Y. L. Tong: Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
 
[10]  M. Tunç: On some new inequalities for convex fonctions, Turk. J. Math. 36 (2012), 245-251.
 
[11]  B.-Y. Xi, R.-F. Bai and F. Qi: Hermite-Hadamard type inequalities for the m- and (α;m)-geometrically convex functions. Aequationes Math.
 
[12]  T.-Y. Zhang, A.-P. Ji and F. Qi: On Integral nequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions. Abstract and Applied Analysis.
 
[13]  T.-Y. Zhang, M. Tunç, A.-P. Ji, B.-Y. Xi: Erratum to. On Integral Inequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions. Abstract and Applied Analysis. Volume 2014, Article ID 294739, 5 pages.