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Dergiler / New Trends in Mathematical Sciences / 2017 / Cilt: 5 Sayı: 2

Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions

Imdat Iscan
Huriye KADAKAL
Mahir KADAKAL
Sayfa
180–185
Yayın Tarihi
2017-03-30
DOI
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In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.
📊
Temel Bulgular & Veri:In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.
💡
Sonuç & Katkı:In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Convex function · m)-convex function

Abstract

In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.

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Bu Makaleye Atıf Yap

Iscan, I., KADAKAL, H., KADAKAL, M. (2017). Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences, Cilt: 5 Sayı: 2, 180–185. https://ajindex.com/articles/1003741

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Kaynakça (8)

  1. S.P. Bai, S.H. Wang and F. Qi, “Some Hermite-Hadamard type inequalities for n-time differentiable (a,m)-convex functions”, Jour. of Ineq. and Appl., 2012, 2012:267. M. K. Bakula, M. E. ¨Ozdemir and J. Pecaric, “Hadamard type inequalities for m-convex and (a, m)-convex functions”, J. Inequal. Pure & Appl. Math., 9(2008), Article 96, [http://jipam.vu.edu.au].
  2. P. Cerone, S.S. Dragomir and J. Roumeliotis, “Some Ostrowski type inequalities for n-time differentiable mappings and applications”, Demonstratio Math., 32 (4) (1999), 697–712.
  3. P. Cerone, S.S. Dragomir, J. Roumeliotis and J. Sunde, “A new generalization of the trapezoid formula for n-time differentiable mappings and applications”, Demonstratio Math., 33 (4) (2000), 719–736. S.S. Dragomir and C.E.M. Pearce, “Selected Topics on Hermite-Hadamard Inequalities and Applications”, RGMIA Monographs, Victoria University, 2000, online: http://www.staxo.vu.edu.au/RGMIA/monographs/hermitehadamard.html. D.Y. Hwang, “Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335–343. I. Iscan, “Ostrowski type inequalities for p-convex functions”, New Trends in Mathematical Sciences, 4 (3) (2016), 140-150. I. Iscan and S. Turhan, “Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral”, Moroccan J. Pure and Appl. Anal.(MJPAA), Volume 2(1) (2016), 34-46. I. Iscan, “Hermite-Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935–942.
  4. I. Iscan, A new generalization of some integral inequalities for (a,m)-convex functions, Mathematical Sciences 2013, 7:22,1-8, doi:10.1186/2251-7456-7-22.
  5. I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are (a,m)-convex, International Journal of Engineering and Applied sciences (EAAS), 2 (3) (2013), 69-78.
  6. I. Iscan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, International Journal of Pure and Applied Mathematics, 86 (4) (2013), 727-746.
  7. I. Iscan, New estimates on generalization of some integral inequalities for (a,m)-convex functions, Contemporary Analysis and Applied Mathematics, Vol. 1, No. 2 (2013), 253-264.
  8. M. Kadakal, H. Kadakaland, I. Iscan, “Some New Integral Inequalities for n- Times Differentiable s-Convex Functions in the First Sense”, Turkish Journal of Analysis and Number Theory, 2017, (Accepted). M. Klaricic, Bakula,