SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS

M. Esra Yıldırım; Abdullah Akkurt; Hüseyin Yıldırım

Araştırma Makalesi

SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS

Yıl 2016, Cilt: 4 Sayı: 2, 1 - 9, 15.10.2016

M. Esra Yıldırım Abdullah Akkurt Hüseyin Yıldırım

Öz

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.

Anahtar Kelimeler

Hermite--Hadamard inequality; Riemann--Liouville fractional integral, h-convex functions

Kaynakça

[1] Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
[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

Yıl 2016, Cilt: 4 Sayı: 2, 1 - 9, 15.10.2016

M. Esra Yıldırım Abdullah Akkurt Hüseyin Yıldırım

Öz

Kaynakça

[1] Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
[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

Toplam 21 adet kaynakça vardır.

Ayrıntılar

Konular	Mühendislik
Bölüm	Articles
Yazarlar	M. Esra Yıldırım Bu kişi benim Abdullah Akkurt Hüseyin Yıldırım
Yayımlanma Tarihi	15 Ekim 2016
Gönderilme Tarihi	16 Ekim 2017
Kabul Tarihi	6 Temmuz 2016
Yayımlandığı Sayı	Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA	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. Ekim 2016;4(2):1-9.
Chicago	Yıldırım, M. Esra, Abdullah Akkurt, ve Hüseyin Yıldırım. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 1-9.
EndNote	Yıldırım ME, Akkurt A, Yıldırım H (01 Ekim 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, ve H. Yıldırım, “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”, Konuralp J. Math., c. 4, sy. 2, ss. 1–9, 2016.
ISNAD	Yıldırım, M. Esra vd. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (Ekim 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 vd. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 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.

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