ON NEW INEQUALITIES OF HERMITE-HADAMARD-FEJER TYPE FOR GA-s CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2016, Volume: 4 Issue: 1, 130 - 139, 01.04.2016

Mehmet Kunt İmdat İşcan

Abstract

In this paper, some Hermite-Hadamard-Fejer type integral in- equalities for GA-s convex functions in fractional integral forms are obtained.

Keywords

Hermite-Hadamard inequality, Hermite-Hadamard-Fejer inequality, Hadamard fractional integral, GA-s convex function

References

• [1] L. Fejer, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24 (1906), 369-390, (in Hungarian).
• [2] J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d'une fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
• [3] _I. _ Iscan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional inte- grals, arXiv preprint arXiv:1404.7722 (2014).
• [4] _I. _ Iscan, Generalization of dierent type integral inequalities for s-convex functions via frac- tional integrals, Applicable Analysis, 2013. doi: 10.1080/00036811.2013.851785.
• [5] _I. _ Iscan, New general integral inequalities for quasi-geometrically convex functions via frac- tional integrals, J. Inequal. Appl., 2013(491) (2013), 15 pages.
• [6] _I. _ Iscan, On generalization of dierent type integral inequalities for s-convex functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 2(1) (2014), 55-67.
• [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional dierential equations, Elsevier, Amsterdam 2006.
• [8] M. Kunt, _I. _ Iscan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex func- tions via fractional integrals, RGMIA Research Report Collection, 18(2015), Article 108, 12 pp.
• [9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometrically-arithmetically-convex functions with applications, RGMIA Research Report Collection, 18(2015), Article 25, 18 pp.
• [10] C. P. Niculescu, Convexity according to the geometric mean, Math. Inequal. Appl. 3 (2) (2000), 155-167.
• [11] C. P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (4) (2003), 571-579.
• [12] M.Z. Sarkaya, On new Hermite Hadamard Fejer type integral inequalities, Stud. Univ. Babes- Bolyai Math. 57(3) (2012), 377-386.
• [13] Erhan Set, _I. _ Iscan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite- Hadamard-Fejer type for convex functions via fractional integrals, Applied Mathematics and Computation, 259 (2015) 875-881.
• [14] Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometrically- arithmetically s-convex functions, Analysis (Munich) 33 (2) (2013) 197-208.
• [15] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for dierentiable mappings and applications to Fejer inequality and weighted trapezoidal formula, Taiwanese journal of Math- ematics, 15(4) (2011), 1737-1747.
• [16] J. Wang, X. Li, M. Feckan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann- Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92(11) (2012), 2241-2253.
• [17] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013(325) (2013), 15 pages.