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Year 2020, Volume: 8 Issue: 1, 91 - 96, 15.04.2020

Abstract

Supporting Institution

Yok

Project Number

Yok

References

  • [1] B. Martos, The Power of Nonlinear Programming Methods (In Hungarian). MTA Kozgazdas agtudom anyi Int ezet enek Kozlem enyei, No. 20, Budapest, Hungary, 1966.
  • [2] M. Avriel, r–Convex Functions, Mathematical Programming, 2 (1972), 309-323.
  • [3] S. S. Dragomir, C.E.M. Pearse, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000, [ONLINE. http://rgmia.org /papers/monographs/Master.pdf]
  • [4] M. Z. Sarıkaya, A. Saglam and H. Yıldırım, On some Hadamard-type inequalities for h􀀀convex functions, J. Math. Inequal. 2 (2008), 335–341.
  • [5] L. Chun and F. Qi, Integral inequalities of Hermite–Hadamard type for functions whose third derivatives are convex. Journal of Inequalities and Applications. 2013:451.(2013)
  • [6] S.. Wu, B. Sroysang, J.-S. Xie and Y.-M. Chu, Parametrized inequality of Hermite–Hadamard type for functions whose third derivative absolute values are quasi-convex, Wu et al. SpringerPlus. 4:831 (2015) Page 9 of 9.
  • [7] I. Iscan, Hermite-Hadamard type inequalities for harmonically (alpha;m)convex functions, J. Hacettepe of Mathematics and Statistics 45 (2016) 2, 381–390. [8] J., Materano, N., Merentes and M., Valera–Lopez, On Inequalities Of Hermite–Hadamard Type for Stochastic Processes Whose Third Derivative Absolute Values Are Quasi–Convex, Tamkang Journal Of Mathematics. 48 (2017) 2, 203–208.
  • [9] B. Bayraktar and M. Gurbuz, On some integral inequalities for (s;m)􀀀convex functions, TWMS J. App. Eng. Math., 10(2) (2020), 288–295.
  • [10] M. A. Noor, K. I. Noor and F. Safdar, New inequalities for generalized Log h􀀀convex functions, J. Appl. Math.& Informatics 36 (2018), 3–4,245– 256
  • [11] E. Set, M.E. O¨ zdemir, N. Korkut, On New Fractional Hermite–Hadamard Type Inequalities for (nal pha;m)-Convex Function, Konuralp Journal of Mathematics, 7(1) (2019), 62–72
  • [12] B. Bayraktar and V. Kudaev, Some new integral inequalities for (s;m)􀀀convex and (a;m)-convex functions, Bulletin of the Karganda University- Mathematics, 94(2) (2019), 15–25.
  • [13] J. Hadamard, E´tude sur les proprie´te´s des fonctions entie`res en particulier d’une fonction conside´re´e par Riemann. J. Math. Pures Appl. 58 (1893), 171–215.
  • [14] E. K. Godunova and V. I. Levin: Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian) Numerical mathematics and mathematical physics (Russian), 138-142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985.
  • [15] S. S. Dragomir, J. Peˇcari´c and L. Persson, Some Inequalities of Hadamard Type. Soochow J. Math. 21(3) (1995), 335–341.
  • [16] A. O. Akdemir, M. E. O¨ zdemir, S. Varosanec, On some inequalities for h–concave functions, Mathematical and Computer Modelling 55 (2012) 746–753.
  • [17] M. E. O¨ zdemir, M. Tunc , and H. Kavurmaci, Two New Different Kinds of Convex Dominated Functions and Inequalties Via Hermite–Hadamard Type, arXiv:1202.2055v1[math.CA] 9 Feb 2012
  • [18] M. D. Noor, K.A. Noor, M. U. Awan, S.Khan, Hermite–Hadamard Inequalities For s–Godunova–Levin Preinvex Functions, J. Adv. Math. Stud. 7(2) (2014) 12–19.
  • [19] M. A. Noor, K. I. Noor, M. U. Awan and S. Khan, Fractional Hermite–Hadamard Inequalities for some New Classes of Godunova–Levin Functions, Appl. Math. Inf. Sci.8(6) (2014), 2865–2872.
  • [20] M. E. Ozdemir, Some inequalities for the s-Godunova–Levin type functions, Math Sci 9 (2015) 27–32.
  • [21] M. Li, J. Wang, W. Wei, Some Fractional Hermite–Hadamard Inequalities for Convex and Godunova–Levin Functions, FACTA UNIVERSITATIS (NIˆ S) Ser. Math. Inform. 30(2) (2015), 195–208.
  • [22] M. U. Awan, M. A. Noor, M. V. Mihai, K. I. Noor, Fractional Hermite–Hadamard Inequalities for Differentiable s–Godunova–Levin Functions, Filomat, 30(12)(2016), 3235–3241.
  • [23] S. Miller and B. Ross, (1993). An introduction to the Fractional Calculus and Fractional Differential Equations. USA: John Wiley & Sons, p.2.
  • [24] B. Bayraktar, Some Integral Inequalities Of Hermite–Hadamard Type For Differentiable (s;m)–Convex Functions Via Fractional Integrals, TWMS J. App. Eng. Math. Accepted, 2019.

Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals

Year 2020, Volume: 8 Issue: 1, 91 - 96, 15.04.2020

Abstract

In this paper, we present new inequalities of the Hermite -– Hadamard type related to fractional integrals for Godunova-- Levin type functions. These inequalities are obtained with the help the of definitions of the Godunova-–Levin functions, the Holder and Power mean type inequalities.

Project Number

Yok

References

  • [1] B. Martos, The Power of Nonlinear Programming Methods (In Hungarian). MTA Kozgazdas agtudom anyi Int ezet enek Kozlem enyei, No. 20, Budapest, Hungary, 1966.
  • [2] M. Avriel, r–Convex Functions, Mathematical Programming, 2 (1972), 309-323.
  • [3] S. S. Dragomir, C.E.M. Pearse, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000, [ONLINE. http://rgmia.org /papers/monographs/Master.pdf]
  • [4] M. Z. Sarıkaya, A. Saglam and H. Yıldırım, On some Hadamard-type inequalities for h􀀀convex functions, J. Math. Inequal. 2 (2008), 335–341.
  • [5] L. Chun and F. Qi, Integral inequalities of Hermite–Hadamard type for functions whose third derivatives are convex. Journal of Inequalities and Applications. 2013:451.(2013)
  • [6] S.. Wu, B. Sroysang, J.-S. Xie and Y.-M. Chu, Parametrized inequality of Hermite–Hadamard type for functions whose third derivative absolute values are quasi-convex, Wu et al. SpringerPlus. 4:831 (2015) Page 9 of 9.
  • [7] I. Iscan, Hermite-Hadamard type inequalities for harmonically (alpha;m)convex functions, J. Hacettepe of Mathematics and Statistics 45 (2016) 2, 381–390. [8] J., Materano, N., Merentes and M., Valera–Lopez, On Inequalities Of Hermite–Hadamard Type for Stochastic Processes Whose Third Derivative Absolute Values Are Quasi–Convex, Tamkang Journal Of Mathematics. 48 (2017) 2, 203–208.
  • [9] B. Bayraktar and M. Gurbuz, On some integral inequalities for (s;m)􀀀convex functions, TWMS J. App. Eng. Math., 10(2) (2020), 288–295.
  • [10] M. A. Noor, K. I. Noor and F. Safdar, New inequalities for generalized Log h􀀀convex functions, J. Appl. Math.& Informatics 36 (2018), 3–4,245– 256
  • [11] E. Set, M.E. O¨ zdemir, N. Korkut, On New Fractional Hermite–Hadamard Type Inequalities for (nal pha;m)-Convex Function, Konuralp Journal of Mathematics, 7(1) (2019), 62–72
  • [12] B. Bayraktar and V. Kudaev, Some new integral inequalities for (s;m)􀀀convex and (a;m)-convex functions, Bulletin of the Karganda University- Mathematics, 94(2) (2019), 15–25.
  • [13] J. Hadamard, E´tude sur les proprie´te´s des fonctions entie`res en particulier d’une fonction conside´re´e par Riemann. J. Math. Pures Appl. 58 (1893), 171–215.
  • [14] E. K. Godunova and V. I. Levin: Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions. (Russian) Numerical mathematics and mathematical physics (Russian), 138-142, 166, Moskov. Gos. Ped. Inst., Moscow, 1985.
  • [15] S. S. Dragomir, J. Peˇcari´c and L. Persson, Some Inequalities of Hadamard Type. Soochow J. Math. 21(3) (1995), 335–341.
  • [16] A. O. Akdemir, M. E. O¨ zdemir, S. Varosanec, On some inequalities for h–concave functions, Mathematical and Computer Modelling 55 (2012) 746–753.
  • [17] M. E. O¨ zdemir, M. Tunc , and H. Kavurmaci, Two New Different Kinds of Convex Dominated Functions and Inequalties Via Hermite–Hadamard Type, arXiv:1202.2055v1[math.CA] 9 Feb 2012
  • [18] M. D. Noor, K.A. Noor, M. U. Awan, S.Khan, Hermite–Hadamard Inequalities For s–Godunova–Levin Preinvex Functions, J. Adv. Math. Stud. 7(2) (2014) 12–19.
  • [19] M. A. Noor, K. I. Noor, M. U. Awan and S. Khan, Fractional Hermite–Hadamard Inequalities for some New Classes of Godunova–Levin Functions, Appl. Math. Inf. Sci.8(6) (2014), 2865–2872.
  • [20] M. E. Ozdemir, Some inequalities for the s-Godunova–Levin type functions, Math Sci 9 (2015) 27–32.
  • [21] M. Li, J. Wang, W. Wei, Some Fractional Hermite–Hadamard Inequalities for Convex and Godunova–Levin Functions, FACTA UNIVERSITATIS (NIˆ S) Ser. Math. Inform. 30(2) (2015), 195–208.
  • [22] M. U. Awan, M. A. Noor, M. V. Mihai, K. I. Noor, Fractional Hermite–Hadamard Inequalities for Differentiable s–Godunova–Levin Functions, Filomat, 30(12)(2016), 3235–3241.
  • [23] S. Miller and B. Ross, (1993). An introduction to the Fractional Calculus and Fractional Differential Equations. USA: John Wiley & Sons, p.2.
  • [24] B. Bayraktar, Some Integral Inequalities Of Hermite–Hadamard Type For Differentiable (s;m)–Convex Functions Via Fractional Integrals, TWMS J. App. Eng. Math. Accepted, 2019.
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bahtiyar Bayraktar

Project Number Yok
Publication Date April 15, 2020
Submission Date July 2, 2019
Acceptance Date February 24, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Bayraktar, B. (2020). Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals. Konuralp Journal of Mathematics, 8(1), 91-96.
AMA Bayraktar B. Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals. Konuralp J. Math. April 2020;8(1):91-96.
Chicago Bayraktar, Bahtiyar. “Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 91-96.
EndNote Bayraktar B (April 1, 2020) Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals. Konuralp Journal of Mathematics 8 1 91–96.
IEEE B. Bayraktar, “Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals”, Konuralp J. Math., vol. 8, no. 1, pp. 91–96, 2020.
ISNAD Bayraktar, Bahtiyar. “Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals”. Konuralp Journal of Mathematics 8/1 (April 2020), 91-96.
JAMA Bayraktar B. Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals. Konuralp J. Math. 2020;8:91–96.
MLA Bayraktar, Bahtiyar. “Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 91-96.
Vancouver Bayraktar B. Some New Inequalities of Hermite-Hadamard Type for Differentiable Godunova-Levin Functions via Fractional Integrals. Konuralp J. Math. 2020;8(1):91-6.
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