In this paper, we obtain new estimates on generalization of Hermite-Hadamard type inequalities for functions whose second derivatives is $\varphi -$ convex via fractional integrals.
[2] Dahmani, Z. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(2010), no. 1, 51-58.
[3] Dragomir, S. S., Inequalities of Jensen type for '-convex functions, Fasc. Math. 55(2015), 35-52.
[4] Hudzik H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1994), no. 1, 100-111.
[5] Işcan, I., Bekar, K. and Numan, S., Hermite-Hadamard an Simpson type inequalities for diFFerentiable quasi-geometrically convex func- tions, Turkish J: of Anal. and Number Theory, 2(2014), no. 2, 42-46.
[6] Işcan, I., New estimates on generalization of some integral inequalities for ds-convex functions and their applications, Int. J. Pure Appl. Math., 86(2013), no. 4, 727-746.
[7] Işcan, I., Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute value are quasi-convex Konuralp Journal of Mathematics, 1(2013), no. 2, 67-79.
[8] Işcan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals presented
[9] Kavurmaci, H., Avci, M. and Ozdemir, M. E., New inequalities of Hermite- Hadamard's type for convex functions with applications, Journ. of Inequal. and Appl., 2011:86 (2011).
[10] Mihesan, V. G., A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex, Cluj-Napoca, Romania (1993).
[11] Ozdemir, M. E., Avic, M. and Kavurmaci, H., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, arXiv:1202.0380v1[math.CA].
[12] Park, J., Some new Hermite-Hadamard-like type inequalities on geometrically convex functions, Inter. J. of Math. Anal., 8(16) (2014),793-802.
[13] Park, J., On Some Integral Inequalities for Twice Differentiable Quasi-Convex and Convex Functions via Fractional Integrals, Applied Mathematical Sciences, Vol. 9(62) (2015), 3057-3069 HIKARI Ltd, www.m-hikari.com.
http://dx.doi.org/10.12988/ams.2015.53248.
[14] Samko, S.G., Kilbas A.A. and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, 1993, ISBN 2881248640.
[15] Sarikaya, M. Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract and applied analysis, 2012 (2012) 10 pages.
[16] Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N., Hermite- Hadamard's inequalities for fractional integrals and related frac- tional inequalities, Math. and Comput. Model., 2011 (2011).
[17] Set, E., Sarikaya, M. Z. and Ozdemir, M. E., Some Ostrowski's type Inequalities for functions whose second derivatives are s-convex in the second sense, arXiv:1006.24 88v1 [math. CA] 12 June 2010.
[18] Set, E., Ozdemir, M. E., Sarikaya M. Z., Karako, F., Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals, Khayyam J. Math., 1(1) (2015) 62-70.
[19] Toader, Gh., On a generalization of the convexity, Mathematica, 30(53) (1988), 83-87.
[20] Tunc, M., On some new inequalities for convex functions, Turk. J. Math., 35(2011), 1-7.
[21] Tunc, M. and Yildirim, H., On MT-Convexity, arXiv: 1205.5453 [math. CA] 24 May 2012
[2] Dahmani, Z. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(2010), no. 1, 51-58.
[3] Dragomir, S. S., Inequalities of Jensen type for '-convex functions, Fasc. Math. 55(2015), 35-52.
[4] Hudzik H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1994), no. 1, 100-111.
[5] Işcan, I., Bekar, K. and Numan, S., Hermite-Hadamard an Simpson type inequalities for diFFerentiable quasi-geometrically convex func- tions, Turkish J: of Anal. and Number Theory, 2(2014), no. 2, 42-46.
[6] Işcan, I., New estimates on generalization of some integral inequalities for ds-convex functions and their applications, Int. J. Pure Appl. Math., 86(2013), no. 4, 727-746.
[7] Işcan, I., Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute value are quasi-convex Konuralp Journal of Mathematics, 1(2013), no. 2, 67-79.
[8] Işcan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals presented
[9] Kavurmaci, H., Avci, M. and Ozdemir, M. E., New inequalities of Hermite- Hadamard's type for convex functions with applications, Journ. of Inequal. and Appl., 2011:86 (2011).
[10] Mihesan, V. G., A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex, Cluj-Napoca, Romania (1993).
[11] Ozdemir, M. E., Avic, M. and Kavurmaci, H., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, arXiv:1202.0380v1[math.CA].
[12] Park, J., Some new Hermite-Hadamard-like type inequalities on geometrically convex functions, Inter. J. of Math. Anal., 8(16) (2014),793-802.
[13] Park, J., On Some Integral Inequalities for Twice Differentiable Quasi-Convex and Convex Functions via Fractional Integrals, Applied Mathematical Sciences, Vol. 9(62) (2015), 3057-3069 HIKARI Ltd, www.m-hikari.com.
http://dx.doi.org/10.12988/ams.2015.53248.
[14] Samko, S.G., Kilbas A.A. and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, 1993, ISBN 2881248640.
[15] Sarikaya, M. Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract and applied analysis, 2012 (2012) 10 pages.
[16] Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N., Hermite- Hadamard's inequalities for fractional integrals and related frac- tional inequalities, Math. and Comput. Model., 2011 (2011).
[17] Set, E., Sarikaya, M. Z. and Ozdemir, M. E., Some Ostrowski's type Inequalities for functions whose second derivatives are s-convex in the second sense, arXiv:1006.24 88v1 [math. CA] 12 June 2010.
[18] Set, E., Ozdemir, M. E., Sarikaya M. Z., Karako, F., Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals, Khayyam J. Math., 1(1) (2015) 62-70.
[19] Toader, Gh., On a generalization of the convexity, Mathematica, 30(53) (1988), 83-87.
[20] Tunc, M., On some new inequalities for convex functions, Turk. J. Math., 35(2011), 1-7.
[21] Tunc, M. and Yildirim, H., On MT-Convexity, arXiv: 1205.5453 [math. CA] 24 May 2012
Yıldırım, M. E., Akkurt, A., & Yıldırım, H. (2016). SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(2), 1-9.
AMA
Yıldırım ME, Akkurt A, Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. October 2016;4(2):1-9.
Chicago
Yıldırım, M. Esra, Abdullah Akkurt, and Hüseyin Yıldırım. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 1-9.
EndNote
Yıldırım ME, Akkurt A, Yıldırım H (October 1, 2016) SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 2 1–9.
IEEE
M. E. Yıldırım, A. Akkurt, and H. Yıldırım, “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 4, no. 2, pp. 1–9, 2016.
ISNAD
Yıldırım, M. Esra et al. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (October 2016), 1-9.
JAMA
Yıldırım ME, Akkurt A, Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:1–9.
MLA
Yıldırım, M. Esra et al. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 1-9.
Vancouver
Yıldırım ME, Akkurt A, Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(2):1-9.