Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals
Keywords:
Hermite-Hadamard inequality, Hermite-Hadamard-Fejér inequality, Riemann-Liouville fractional integral, convex function.Abstract
In this paper, firstly we have established Hermite-Hadamard-Fejér inequality for fractional integrals. Secondly, an integral identity and some Hermite-Hadamard-Fejér type integral inequalities for the fractional integrals have been obtained. The some results presented here would provide extensions of those given in earlier works.
Mathematics Subject Classification (2010): 26A51, 26A33, 26D10.
References
Bombardelli, M., Varosanec, S., Properties of h-convex functions related to the Hermite Hadamard Fejer inequalities, Computers and Mathematics with Applications, 58(2009), 1869-1877.
Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional via fractional integration, Ann. Funct. Anal. 1(1)(2010), 51-58.
Fejer, L., Uberdie Fourierreihen, II, Math., Naturwise. Anz Ungar. Akad. Wiss, 24(1906), 369-390, (in Hungarian).
Hadamard, J., Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58(1893), 171-215.
Iscan, I., New estimates on generalization of some integral inequalities for (α;m)-convex functions, Contemp. Anal. Appl. Math., 1(2)(2013), 253-264.
Iscan, I., New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., 86(4)(2013), 727-746.
Iscan, I., Some new general integral inequalities for h-convex and h-concave functions, Adv. Pure Appl. Math., 5(1)(2014), 21-29, doi: 10.1515/apam-2013-0029.
Iscan, I., Generalization of different type integral inequalities for s-convex functions via fractional integrals, Applicable Analysis, 93(9)(2014), 1846-1862.
Iscan, I., New general integral inequalities for quasi-geometrically convex functions via fractional integrals, J. Inequal. Appl., 2013(491)(2013), 15 pages.
Iscan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1)(2014), 55-67.
Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I., Integral and series. In: Elementary Functions, vol. 1, Nauka, Moscow, 1981.
Sarkaya, M.Z., On new Hermite Hadamard Fejer type integral inequalities, Stud. Univ. Babes-Bolyai Math. 57(2012), no. 3, 377-386.
Sarkaya, M.Z., Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract an Applied Analysis, 2012(2012), 10 pages, Article ID 428983. doi:10.1155/2012/428983
Sarkaya, M.Z., Set, E., Yaldz, H., Basak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57(9)(2013), 2403-2407.
Set, E., New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Computers and Math. with Appl., 63(2012), 1147-1154.
Tseng, K.-L., Yang, G.-S., Hsu, K.-C., Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese journal of Mathematics, 15(4)(2011), 1737-1747.
Wang, J., Li, X., Feckan, M., Zhou, Y., Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11)(2012), 2241-2253. doi:10.1080/00036811.2012.727986
Wang, J., Zhu, C., Zhou, Y., New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325)(2013), 15 pages.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
