Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 41 Sayı: 1, 69 - 84, 22.03.2020
https://doi.org/10.17776/csj.538397

Öz

Kaynakça

  • [1] Dragomir, S.S., Pečarić, J. and Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21 (1995) 335-341.
  • [2] Dragomir, S.S. and Mond, B., Integral inequalities of Hadamard’s type for log-convex functions, Demonstration Math., 2 (1998) 354-364.
  • [3] Noor, M.A., Noor, K.I. and Awan, M.U., Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17(1) (2014) 51-61.
  • [4] Noor, M.A., Noor, K.I. and Awan, M.U., Some integral inequalities for harmonically logarithmic -convex functions, Preprint, (2014).
  • [5] Noor, M.A., Noor, K.I., Awan, M.U. and Khan, S., Fractional Hermite-Hadamard inequalities for some new classes of Godunova-Levin functions, Appl. Math. Infor. Sci., 8(6) (2014).
  • [6] Noor, M.A., Noor, K.I., Awan, M.U. and Costache, S., Some integral inequalities for harmonically -convex functions, U. P. B. Sci. Bull., Series A., 77(1) (2015) 5-16.
  • [7] Sarikaya, M.Z., Saglam, A. and Yildirim, H., On some Hadamard-type inequalities for -convex functions, Jour. Math. Ineq., 2(3) (2008) 335-341.
  • [8] Sarikaya, M.Z., Set, E. and Ozdemir, M.E., On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae, 2 (2010) 265-272.
  • [9] Varosanec, S., On -convexity, Jour. Math. Anal. Appl., 326 (2007) 303-311.
  • [10] http://arxiv.org/abs/1303.6089, (25.03.2013).

First order derivatives new h.hadamard type ınequalities for harmonically h convex functions

Yıl 2020, Cilt: 41 Sayı: 1, 69 - 84, 22.03.2020
https://doi.org/10.17776/csj.538397

Öz

In this study, we derived a new integral identity for differentiable functions. However, we get new inequalities which is well known as Hermite-Hadamard (H-H) type by using the integral identity, which unifies the class of new and known harmonically convex functions. Moreover, in this study, the properties of first and second kind harmonically s-convex and harmonically s-Godunova-Levin functions are studied and some special cases are also dealt. Some important inferences are made at this study for supporting the results that obtained for classes of harmonically convex functions in previous studies. 

Kaynakça

  • [1] Dragomir, S.S., Pečarić, J. and Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21 (1995) 335-341.
  • [2] Dragomir, S.S. and Mond, B., Integral inequalities of Hadamard’s type for log-convex functions, Demonstration Math., 2 (1998) 354-364.
  • [3] Noor, M.A., Noor, K.I. and Awan, M.U., Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17(1) (2014) 51-61.
  • [4] Noor, M.A., Noor, K.I. and Awan, M.U., Some integral inequalities for harmonically logarithmic -convex functions, Preprint, (2014).
  • [5] Noor, M.A., Noor, K.I., Awan, M.U. and Khan, S., Fractional Hermite-Hadamard inequalities for some new classes of Godunova-Levin functions, Appl. Math. Infor. Sci., 8(6) (2014).
  • [6] Noor, M.A., Noor, K.I., Awan, M.U. and Costache, S., Some integral inequalities for harmonically -convex functions, U. P. B. Sci. Bull., Series A., 77(1) (2015) 5-16.
  • [7] Sarikaya, M.Z., Saglam, A. and Yildirim, H., On some Hadamard-type inequalities for -convex functions, Jour. Math. Ineq., 2(3) (2008) 335-341.
  • [8] Sarikaya, M.Z., Set, E. and Ozdemir, M.E., On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae, 2 (2010) 265-272.
  • [9] Varosanec, S., On -convexity, Jour. Math. Anal. Appl., 326 (2007) 303-311.
  • [10] http://arxiv.org/abs/1303.6089, (25.03.2013).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Natural Sciences
Yazarlar

Merve Kule 0000-0001-8144-7768

Mehmet Eyüp Kiriş 0000-0001-8144-7768

Yayımlanma Tarihi 22 Mart 2020
Gönderilme Tarihi 11 Mart 2019
Kabul Tarihi 27 Haziran 2019
Yayımlandığı Sayı Yıl 2020Cilt: 41 Sayı: 1

Kaynak Göster

APA Kule, M., & Kiriş, M. E. (2020). First order derivatives new h.hadamard type ınequalities for harmonically h convex functions. Cumhuriyet Science Journal, 41(1), 69-84. https://doi.org/10.17776/csj.538397