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Year 2019, Volume: 7 Issue: 2, 442 - 448, 15.10.2019

Huriye Kadakal Kerim Bekar

Abstract

References

  • [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

Year 2019, Volume: 7 Issue: 2, 442 - 448, 15.10.2019

Huriye Kadakal Kerim Bekar

Abstract

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.

Keywords

Convex function AH-convex function Hermite-Hadamard and Bullen type inequality

References

  • [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.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Huriye Kadakal 0000-0002-0304-7192

Kerim Bekar 0000-0002-7531-9345

Publication Date October 15, 2019
Submission Date April 30, 2019
Acceptance Date September 20, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

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. October 2019;7(2):442-448.
Chicago Kadakal, Huriye, and Kerim Bekar. “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 442-48.
EndNote Kadakal H, Bekar K (October 1, 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 and K. Bekar, “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”, Konuralp J. Math., vol. 7, no. 2, pp. 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 (October 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 and Kerim Bekar. “Inequalities of Hermite-Hadamard and Bullen Type for Three Times Differentiable $AH$-Convex Functions”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 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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