Research Article

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

Volume: 3 Number: 3 September 29, 2020
EN

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

Abstract

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.                                                                                                                                                                                                                                                                                                                                                                                                                 

Keywords

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

References

  1. [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. [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. [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  4. [4] D.Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. Jour., 43 (2003), 335–343.
  5. [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. [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. [7] İ. İşcan, New refinements for integral and sum forms of H¨older inequality, J. Inequal. Appl., (2019) 2019:304, 11 pages.
  8. [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. [9] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Info., 28(2), (2018), 19-28.
  10. [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.
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
1.Bekar K. Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Univ. J. Math. Appl. 2020;3(3):109-114. doi:10.32323/ujma.652513
Chicago
Bekar, Kerim. 2020. “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”. Universal Journal of Mathematics and Applications 3 (3): 109-14. https://doi.org/10.32323/ujma.652513.
EndNote
Bekar K (September 1, 2020) Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Universal Journal of Mathematics and Applications 3 3 109–114.
IEEE
[1]K. Bekar, “Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions”, Univ. J. Math. Appl., vol. 3, no. 3, pp. 109–114, Sept. 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 (September 1, 2020): 109-114. https://doi.org/10.32323/ujma.652513.
JAMA
1.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, vol. 3, no. 3, Sept. 2020, pp. 109-14, doi:10.32323/ujma.652513.
Vancouver
1.Kerim Bekar. Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions. Univ. J. Math. Appl. 2020 Sep. 1;3(3):109-14. doi:10.32323/ujma.652513