Hermite-Hadamard Type Inequalities for p-Convex Functions

İşcan, İmdat

Research Article

Hermite-Hadamard Type Inequalities for p-Convex Functions

İmdat İşcan¹

Giresun University

Abstract

In this paper, the author establishes some new Hermite-Hadamard type inequalities for p-convex functions. Some natural applications to special means of real numbers are also given.

How to Cite

İ. İşcan, Hermite-Hadamard Type Inequalities for p-Convex Functions, Int. J. Anal. Appl. 11 (2016), 137–145.

BibTeX

@article{İşcan2016,
  author  = {İşcan, İmdat},
  title   = {Hermite-Hadamard Type Inequalities for p-Convex Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {11},
  year    = {2016},
  pages   = {137--145},
  doi     = {}
}

References

[1] G.D. Anderson, M.K. Vamanamurthy and M. Vuorinen, Generalized convexity and inequalities, Journal of Mathematical Analysis and Applications 335(2) (2007), 1294-1308.
[2] M. Avci, H. Kavurmaci and M. E. Ozdemir, New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput., 217 (2011), 5171-5176.
[3] S.S. Dragomir and R.P. Agarwal, Two Inequalities for Differentiable Mappings and Applications to Special Means of Real Numbers and to Trapezoidal Formula, Appl. Math. Lett. 11(5) (1998), 91-95.
[4] Z. B. Fang and R. Shi, On the(p,h)-convex function and some integral inequalities, J. Inequal. Appl., 2014(45) (2014), 16 pages.
[5]Ë™I.Ë™I ¸scan, A new generalization of some integral inequalities for (α,m)-convex functions, Mathematical Sciences,7(22) (2013),1-8.
[6]Ë™I.Ë™I ¸scan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, International Journal of Pure and Applied Mathematics, 86(4) (2013), 727-746.
[7]Ë™I.Ë™I ¸scan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, 43(6) (2014), 935-942.
[8]Ë™I.Ë™I ¸scan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1) (2014), 21-29.
[9]Ë™I.Ë™I ¸scan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, Studia Universitatis Babe ¸s-Bolyai Mathematica, 60(3) (2015), 355-366.
[10]Ë™I.Ë™I ¸scan, Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, in press.
[11] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.
[12] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula,Appl. Math. Comput. 147 (2004), 137-146.
[13] C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl., 3(2) (2000), 155-167.
[14] M. A. Noor, K. I. Noor and S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab University Journal of Mathematics, 47(2) (2015), 19-27.
[15] 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.
[16] K.S. Zhang and J.P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007), 130-133.