Ostrowski type inequalities for p-convex functions

Abstract

In this paper, we give a different version of the concept of -convex functions and obtain some new properties of -convex functions. Moreover we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are -convex.

Keywords

• p-convex function,Ostrowski type inequality

References

1. J. Aczél, A generalization of the notion of convex functions, Norske Vid. Selsk. Forhd., Trondhjem 19(24) (1947), 87–90.
2. M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
3. M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Applied Mathematics Letters 23(9) (2010), 1071-1076.
4. G. Aumann, Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten, Bayer. Akad. Wiss.Math.-Natur. Kl. Abh., Math. Ann. 109 (1933), 405–413.
5. I. A. Baloch and İ. İşcan, Some Ostrowski Type Inequalities For Harmonically (s,m)- convex functoins in Second Sense, International Journal of Analysis, vol. 2015 (2015), Article ID 672675, 9 pages, http://dx.doi.org/10.1155/2015/672675.
6. P. Cerone and S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Mathematica, Warsaw Technical University Institute of Mathematics 37(2) (2004), 299-308.
7. Z. B. Fang, R. Shi, On the (p,h)-convex function and some integral inequalities, J. Inequal. Appl. 2014(45) (2014), 16 pages.
8. İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions. Hacet. J. Math. Stat. 43(6) (2014), 935–942.

9. İ. İşcan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp journal of Mathematics, 3(1)(2015), 63-74.
10. İ. İşcan, Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian Mathematical Society 40(2) (2014), 373-386.
11. İ. İşcan, S. Numan, Ostrowski type inequalities for harmonically quasi-convex functions, Electronic Journal of Mathematical Analysis and Applications 2(2) (2014), 189-198.
12. J. Matkowski, Convex functions with respect to a mean and a characterization of quasi-arithmetic means, Real Anal. Exchange 29 (2003/2004), 229–246.
13. M. V. Mihai, M. A. Noor, K. I. Noor and M. U. Awan, New estimates for trapezoidal like inequalities via differentiable (p,h)-convex functions, Researchgate doi: 10.13140/RG.2.1.5106.5046. Available online at https://www.researchgate.net/publication/282912293.
14. C. P. Niculescu, "Convexity according to the geometric mean", Math. Inequal. Appl. 3(2) (2000), 155-167.
15. C.P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (2003) 571–579.
16. M. A. Noor, K. I. Noor, M. V. Mihai, and M. U. Awan, Hermite-Hadamard inequalities for differentiable p-convex functions using hypergeometric functions, Researchgate doi: 10.13140/RG.2.1.2485.0648. Available online at https://www.researchgate.net/publication/282912282.
17. M. A. Noor, K. I. Noor, S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab University Journal of Mathematics, 47(2) (2015), 19-27.
18. A. Ostrowski, Über die Absolutabweichung einer differentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
19. K. S. Zhang, J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007), 130-133.