Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 2, 442 - 448, 15.10.2019

Öz

Kaynakça

  • [1] K. Bekar, Inequalities for three-times differentiable arithmetic-harmonically functions, Turkish Journal of Analysis and Number Theory, (Accepted for publication), (2019).
  • [2] S.S. Dragomir, Inequalities of Hermite-Hadamard type for AH-convex functions, Stud. Univ. Babes¸-Bolyai Math. 61(4) (2016), 489-502.
  • [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000).
  • [4] İ. İşcan, T. Toplu and F. Yetgin, Some new inequalities on generalization of Hermite-Hadamard and Bullen type inequalities, Kragujevac Journal of Mathematics, (Accepted for publication), (2019).
  • [5] H. Kadakal, New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, (2019).
  • [6] H. Kadakal, Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Sci. J., Vol.40-3 (2019) 670-678.
  • [7] M. Kadakal and İ. İşcan, Some new inequalities for differentiable arithmetic-harmonically convex functions, Comptes Rendus De L’Academie Bulgare Des Sciences, (Submitted to journal), (2019).
  • [8] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. J. Nonlinear Sci. Appl., 10 (2017), 6141-6148.
  • [9] M.Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54, (2011), 2175-2182.
  • [10] F. Yetgin, M. Korkmaz and İ. İşcan, Some new type general integral inequalities for s-convex functions and related results, January (2017), doi: 10.13140/RG.2.2.22315.64805.
  • [11] T.Y. Zhang and F. Qi, Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions, Turkish Journal of Analysis and Number Theory, 2(3) (2014), 60-64.

Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions

Yıl 2019, Cilt: 7 Sayı: 2, 442 - 448, 15.10.2019

Öz

In this paper, after introducing a new integral identity, by using this integral identity we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose third derivatives in absolute value at certain power are arithmetically-harmonically convex. Some applications to special means of real numbers are also given.

Kaynakça

  • [1] K. Bekar, Inequalities for three-times differentiable arithmetic-harmonically functions, Turkish Journal of Analysis and Number Theory, (Accepted for publication), (2019).
  • [2] S.S. Dragomir, Inequalities of Hermite-Hadamard type for AH-convex functions, Stud. Univ. Babes¸-Bolyai Math. 61(4) (2016), 489-502.
  • [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000).
  • [4] İ. İşcan, T. Toplu and F. Yetgin, Some new inequalities on generalization of Hermite-Hadamard and Bullen type inequalities, Kragujevac Journal of Mathematics, (Accepted for publication), (2019).
  • [5] H. Kadakal, New Inequalities for Strongly r-Convex Functions, Journal of Function Spaces, Volume 2019, Article ID 1219237, 10 pages, (2019).
  • [6] H. Kadakal, Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Sci. J., Vol.40-3 (2019) 670-678.
  • [7] M. Kadakal and İ. İşcan, Some new inequalities for differentiable arithmetic-harmonically convex functions, Comptes Rendus De L’Academie Bulgare Des Sciences, (Submitted to journal), (2019).
  • [8] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. J. Nonlinear Sci. Appl., 10 (2017), 6141-6148.
  • [9] M.Z. Sarikaya and N. Aktan, On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, 54, (2011), 2175-2182.
  • [10] F. Yetgin, M. Korkmaz and İ. İşcan, Some new type general integral inequalities for s-convex functions and related results, January (2017), doi: 10.13140/RG.2.2.22315.64805.
  • [11] T.Y. Zhang and F. Qi, Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions, Turkish Journal of Analysis and Number Theory, 2(3) (2014), 60-64.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Huriye Kadakal 0000-0002-0304-7192

Kerim Bekar 0000-0002-7531-9345

Yayımlanma Tarihi 15 Ekim 2019
Gönderilme Tarihi 30 Nisan 2019
Kabul Tarihi 20 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 2

Kaynak Göster

APA Kadakal, H., & Bekar, K. (2019). Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions. Konuralp Journal of Mathematics, 7(2), 442-448.
AMA Kadakal H, Bekar K. Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions. Konuralp J. Math. Ekim 2019;7(2):442-448.
Chicago Kadakal, Huriye, ve Kerim Bekar. “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”. Konuralp Journal of Mathematics 7, sy. 2 (Ekim 2019): 442-48.
EndNote Kadakal H, Bekar K (01 Ekim 2019) Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions. Konuralp Journal of Mathematics 7 2 442–448.
IEEE H. Kadakal ve K. Bekar, “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”, Konuralp J. Math., c. 7, sy. 2, ss. 442–448, 2019.
ISNAD Kadakal, Huriye - Bekar, Kerim. “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”. Konuralp Journal of Mathematics 7/2 (Ekim 2019), 442-448.
JAMA Kadakal H, Bekar K. Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions. Konuralp J. Math. 2019;7:442–448.
MLA Kadakal, Huriye ve Kerim Bekar. “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”. Konuralp Journal of Mathematics, c. 7, sy. 2, 2019, ss. 442-8.
Vancouver Kadakal H, Bekar K. Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions. Konuralp J. Math. 2019;7(2):442-8.
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