In this paper, some new results related to the left-hand side of the Hermite-Hadamard type inequality for harmonically convex functions using Riemann Liouville fractional integrals are obtained.
[1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and dierentiable equations of fractional order", Springer Verlag, Wien,1997,p.223-276
[2] S.G.Samko, A.A.Kilbas, O.I.Marichev, "Fractional Integrals and Derivates Theory and Ap-plication ,Gordon and Breach Science", New York,1993
[3] İ. İşcan and S. Wu, "Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals",Appl. Math. Compt., 238 (2014), 237-244.
[4] İ. İşcan, "Hermite-Hadamard type inequalities for harmonically convex functions", Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
[5] İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis: An Int. J., 93 (9) (2014), 1846{1862.
[6] İ. İşcan, "New general integral inequalities for quasi-geometrically convex functions via fractional integrals", J. Inequal. Appl., 2013(491), 15 pages, 2013.
[7] A. A. Kilbas, H.M. Srivastava HM and J.J. Trujillo, Theory and applications of fractional differential equations, Amsterdam, Elsevier, 2006.
[8] A. P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, 1981.
[9] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, "Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model., 57, 2403-2407, 2013.
[10] E. Set, "New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals", Comput. Math. Appl., 63, 1147-1154, 2012.
[11] 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), 2241-2253, 2012.
[12] J. Wang, C. Zhu and Y. Zhou, "New generalized Hermite-Hadamard type inequalities and
applications to special means", J. Inequal. Appl., 2013(325), 15 pages, 2013.
[1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and dierentiable equations of fractional order", Springer Verlag, Wien,1997,p.223-276
[2] S.G.Samko, A.A.Kilbas, O.I.Marichev, "Fractional Integrals and Derivates Theory and Ap-plication ,Gordon and Breach Science", New York,1993
[3] İ. İşcan and S. Wu, "Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals",Appl. Math. Compt., 238 (2014), 237-244.
[4] İ. İşcan, "Hermite-Hadamard type inequalities for harmonically convex functions", Hacet. J. Math. Stat., 43 (6) (2014), 935-942.
[5] İ. İşcan, Generalization of different type integral inequalitiesfor s-convex functions via fractional integrals, Applicable Analysis: An Int. J., 93 (9) (2014), 1846{1862.
[6] İ. İşcan, "New general integral inequalities for quasi-geometrically convex functions via fractional integrals", J. Inequal. Appl., 2013(491), 15 pages, 2013.
[7] A. A. Kilbas, H.M. Srivastava HM and J.J. Trujillo, Theory and applications of fractional differential equations, Amsterdam, Elsevier, 2006.
[8] A. P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integral and series. In: Elementary Functions, vol. 1. Nauka, Moscow, 1981.
[9] M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, "Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities", Math. Comput. Model., 57, 2403-2407, 2013.
[10] E. Set, "New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals", Comput. Math. Appl., 63, 1147-1154, 2012.
[11] 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), 2241-2253, 2012.
[12] J. Wang, C. Zhu and Y. Zhou, "New generalized Hermite-Hadamard type inequalities and
applications to special means", J. Inequal. Appl., 2013(325), 15 pages, 2013.
Set, E., İşcan, İ., & Zehır, F. (2015). ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 3(1), 42-55.
AMA
Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. Nisan 2015;3(1):42-55.
Chicago
Set, Erhan, İmdat İşcan, ve Fatma Zehır. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 3, sy. 1 (Nisan 2015): 42-55.
EndNote
Set E, İşcan İ, Zehır F (01 Nisan 2015) ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 3 1 42–55.
IEEE
E. Set, İ. İşcan, ve F. Zehır, “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., c. 3, sy. 1, ss. 42–55, 2015.
ISNAD
Set, Erhan vd. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 3/1 (Nisan 2015), 42-55.
JAMA
Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2015;3:42–55.
MLA
Set, Erhan vd. “ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, c. 3, sy. 1, 2015, ss. 42-55.
Vancouver
Set E, İşcan İ, Zehır F. ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2015;3(1):42-55.