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Yıl 2020, Cilt: 3 Sayı: 3, 109 - 114, 29.09.2020

Kerim Bekar

https://doi.org/10.32323/ujma.652513

Öz

Kaynakça

  • [1] M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math, 41 (4), 2010, 353–359.
  • [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] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • [4] D.Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. Jour., 43 (2003), 335–343.
  • [5] İ. İşcan, S. Turhan, S. Maden, Some Hermite-Hadamard-Fejer type inequalities for Harmonically convex functions via Fractional Integral, New Trends Math. Sci., 4 (2) (2016), 1-10.
  • [6] İ. İşcan, M. Kunt, Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, J. Math., Volume 2016, Article ID 6523041, 7 pages.
  • [7] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, J. Inequal. Appl., (2019) 2019:304, 11 pages.
  • [8] W.D. Jiang, D.W. Niu, , Y. Hua and F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense, Analysis (Munich), 32 (2012), 209–220.
  • [9] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Info., 28(2), (2018), 19-28.
  • [10] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. J. Non. Sci. Appl., 10 12,(2017), 6141-6148.
  • [11] S. Özcan, Some Integral Inequalities for Harmonically (a; s)-Convex Functions, J. Funct. Spaces, 2019, Article ID 2394021, 8 pages (2019).
  • [12] S. Özcan, and İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Inequal. Appl., Article number: 2019:201 (2019).
  • [13] J.E. Pecaric, F. Porschan and Y.L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
  • [14] S.H. Wang, B.Y. Xi and F. Qi, Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich), 32 (2012), 247–262.
  • [15] B.Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012, http://dx.doi.org/10.1155/2012/980438.

Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions

Yıl 2020, Cilt: 3 Sayı: 3, 109 - 114, 29.09.2020

Kerim Bekar

https://doi.org/10.32323/ujma.652513

Öz

In this manuscript, by using an integral identity together with both the Hölder, Hölder-İşcan and the Power-mean integral inequalities we obtain several new inequalities for $n$-time differentiable trigonometrically convex functions.                                                                                                                                                                                                                                                                                                                                                                                                                 

Anahtar Kelimeler

Convex function trigonometrically convex function Hölder Integral inequality Power-Mean Integral inequality Hölder-İşcan integral inequality

Kaynakça

  • [1] M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math, 41 (4), 2010, 353–359.
  • [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] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • [4] D.Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. Jour., 43 (2003), 335–343.
  • [5] İ. İşcan, S. Turhan, S. Maden, Some Hermite-Hadamard-Fejer type inequalities for Harmonically convex functions via Fractional Integral, New Trends Math. Sci., 4 (2) (2016), 1-10.
  • [6] İ. İşcan, M. Kunt, Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, J. Math., Volume 2016, Article ID 6523041, 7 pages.
  • [7] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, J. Inequal. Appl., (2019) 2019:304, 11 pages.
  • [8] W.D. Jiang, D.W. Niu, , Y. Hua and F. Qi, Generalizations of Hermite-Hadamard inequality to n-time differentiable function which are s-convex in the second sense, Analysis (Munich), 32 (2012), 209–220.
  • [9] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Info., 28(2), (2018), 19-28.
  • [10] S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, Some new integral inequalities for n-times differentiable convex and concave functions. J. Non. Sci. Appl., 10 12,(2017), 6141-6148.
  • [11] S. Özcan, Some Integral Inequalities for Harmonically (a; s)-Convex Functions, J. Funct. Spaces, 2019, Article ID 2394021, 8 pages (2019).
  • [12] S. Özcan, and İ. İşcan, Some new Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Inequal. Appl., Article number: 2019:201 (2019).
  • [13] J.E. Pecaric, F. Porschan and Y.L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
  • [14] S.H. Wang, B.Y. Xi and F. Qi, Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich), 32 (2012), 247–262.
  • [15] B.Y. Xi and F. Qi, Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012, http://dx.doi.org/10.1155/2012/980438.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Kerim Bekar 0000-0002-7531-9345

Yayımlanma Tarihi 29 Eylül 2020
Gönderilme Tarihi 28 Kasım 2019
Kabul Tarihi 14 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 3

Kaynak Göster

APA Bekar, K. (2020). Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Universal Journal of Mathematics and Applications, 3(3), 109-114. https://doi.org/10.32323/ujma.652513
AMA Bekar K. Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Univ. J. Math. Appl. Eylül 2020;3(3):109-114. doi:10.32323/ujma.652513
Chicago Bekar, Kerim. “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”. Universal Journal of Mathematics and Applications 3, sy. 3 (Eylül 2020): 109-14. https://doi.org/10.32323/ujma.652513.
EndNote Bekar K (01 Eylül 2020) Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Universal Journal of Mathematics and Applications 3 3 109–114.
IEEE K. Bekar, “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”, Univ. J. Math. Appl., c. 3, sy. 3, ss. 109–114, 2020, doi: 10.32323/ujma.652513.
ISNAD Bekar, Kerim. “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”. Universal Journal of Mathematics and Applications 3/3 (Eylül 2020), 109-114. https://doi.org/10.32323/ujma.652513.
JAMA Bekar K. Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Univ. J. Math. Appl. 2020;3:109–114.
MLA Bekar, Kerim. “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”. Universal Journal of Mathematics and Applications, c. 3, sy. 3, 2020, ss. 109-14, doi:10.32323/ujma.652513.
Vancouver Bekar K. Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Univ. J. Math. Appl. 2020;3(3):109-14.
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