Tekin Toplu, Erhan Set, İmdat İşcan, Selahattin Maden

DOI Number
First page
Last page


In this paper, firstly the authors establish Hermite-Hadamard inequality for p-convex functions via Katugampola fractional integrals. Then a new identity involving Katugampola fractional integrals is proved. By using this identity, some new Hermite-Hadamard type inequalities for classes of p-convex functions are obtained.


p-convex function, Hermite-Hadamard type inequalities, Katugampola fractional integrals


p-convex function, Hermite-Hadamard type inequalities, Katugampola fractional integrals.

Full Text:



M. Avci, H. Kavurmaci and M. E. Ozdemir, New inequalities of HermiteHadamard type via s-convex functions in the second sense with applications, Appl. Math. Comput., 217 (2011), 5171-5176.

P. L. Butzer, A. A. Kilbas, and J. J. Trujillo. Compositions of hadamard-type

fractional integration operators and the semigroup property, Journal of Mathematical Analysis and Applications, 269:387-400, 2002.

Z. B. Fang and R. Shi, On the(p; h)-convex function and some integral inequalities, J. Inequal. Appl., 2014(45)(2014), 16 pages.

E. Guariglia, Fractional Derivate of Riemann-Zeta Function: in Fractional Dynamics, Cattani, Srivastava, Yang (Eds.), De Gruyter, pp 357-368,2015.

E. Guariglia and S. Silvestrov, Fractional-Wavelet Analysis of Positive definite

Distributions and Wavelets on D’(C), in Engineering Mathematics II, Silvestrov,

Rancic (Eds), Springer, pp 357-353, 2017.

I. Iscan, A new generalization of some integral inequalities for (α;m)-convex functions, Mathematical Sciences, 7(22) (2013),1-8.

I. Iscan, 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.

I. Iscan, Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math. 5(1)(2014), 21-29.

I. Iscan, Ostrowski type inequalities for p-convex functions, New Trends in Mathematical Sciences, No. 3, 140-150 (2016).

I. Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, Studia UniversitatisBabe s-Bolyai Mathematica, 60(3) (2015), 355-366.

I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions,

Hacettepe Journal of Mathematics and Statistics, 43(6) (2014), 935-942.

I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions,

Hacet. J. Math. Stat. 43 (6) (2014), 935-942.

U.N. Katugampola, New approach to a generalized fractional integral, Appl.

Math. Comput. 218(3)(2011) 860–865.

U.N. Katugampola, New approach to generalized fractional derivatives, Bull.

Math. Anal. Appl. 6(4)(2014) 1–15.

U.N. Katugampola, Mellin transforms of generalized fractional integrals and

derivatives, Appl. Math. Comput. 257(2015)566–580.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier,Amsterdam, 2006.

A. A. Kilbas, Hadamard-type fractional calculus, Journal of Korean Mathematical

Society, 38(6):1191–1204, 2001.

U.S. Kirmaci, Inequalities for differentiable mappings and applications to special

means of real numbers and to midpoint formula,Appl. Math. Comput. 147 (2004),


V. Kiryakova. Generalized fractional calculus and applications, John Wiley and

Sons Inc., New York, 1994.

K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional

diffrential equations, Wiley, New York, 1993.

M. A. Noor, K. I. Noor and S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab University Journal of Mathematics, 47(2) (2015), 19-27.

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.

K. B. Oldham and J. Spanier, The fractional calculus, Academic Press, New York,

A. Prudnikov, Y. Brychkov, O. Marichev, Integral and series. In: Elementary

Functions,vol. 1. Nauka, Moscow; 1981.

S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.

M.Z. Sarıkaya, E. Set, H. Yaldız, N.Basak, Hermite-Hadamard’s inequalities for

fractionalintegrals and related fractional inequalities, Mathematical and Computer Modelling, 57(2013)2403-2407.

G. K. Srinivasan, The gamma function: An Eclectic Tour, Amer. Math. Monthly

, 297-315 (2007).

K.S. Zhang and J.P. Wan, p-convex functions and their properties, Pure Appl.

Math. 23(1) (2007), 130-133..

J. Wang, C. Zhu, Y. Zhou. New generalized Hermite-Hadamard type inequalities

and applications to special means. J. Inequal. Appl. 2013;2013(325):1-15

DOI: https://doi.org/10.22190/FUMI1901149T


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)