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ON SOME NEW INEQUALITIES OF HERMITE-HADAMARD TYPE INVOLVING HARMONICALLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Yıl 2015, Cilt: 3 Sayı: 1, 42 - 55, 01.04.2015

Öz

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.

Kaynakça

  • [1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and di erentiable 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.
Yıl 2015, Cilt: 3 Sayı: 1, 42 - 55, 01.04.2015

Öz

Kaynakça

  • [1] R.Goren o, F.Mainardi, "Fractionalcalculus;integral and di erentiable 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan Set

İmdat İşcan

Fatma Zehır Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

APA 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.
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