Some new integral inequalities for $n$-times differentiable convex and concave functions

Volume 10, Issue 12, pp 6141--6148
Publication Date: December 02, 2017 Submission Date: January 13, 2017
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Authors

Selahattin Maden - Department of Mathematics, Faculty of Sciences and Arts, Ordu University, Ordu, Turkey. Huriye Kadakal - Institute of Science, Ordu University, Ordu, Turkey. Mahir Kadakal - Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Turkey. İmdat İscan - Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Turkey.

Abstract

In this work, by using an integral identity together with both the Holder and the Power-mean integral inequalities we establish several new inequalities for $n$-times differentiable convex and concave mappings.

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ISRP Style

Selahattin Maden, Huriye Kadakal, Mahir Kadakal, İmdat İscan, Some new integral inequalities for $n$-times differentiable convex and concave functions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6141--6148

AMA Style

Maden Selahattin, Kadakal Huriye, Kadakal Mahir, İscan İmdat, Some new integral inequalities for $n$-times differentiable convex and concave functions. J. Nonlinear Sci. Appl. (2017); 10(12):6141--6148

Chicago/Turabian Style

Maden, Selahattin, Kadakal, Huriye, Kadakal, Mahir, İscan, İmdat. "Some new integral inequalities for $n$-times differentiable convex and concave functions." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6141--6148

Keywords

• Convex function
• concave function
• Holder integral inequality
• power-mean integral inequality

•  26A51
•  26D10
•  26D15

References

• [1] M. Alomari, M. Darus, S. S. Dragomir , New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., 41 (2010), 353–359.

• [2] S.-P. Bai, S.-H. Wang, F. Qi , Some Hermite-Hadamard type inequalities for n-time differentiable ($\alpha,m$)-convex functions, J. Inequal. Appl., 2012 (2012), 11 pages.

• [3] P. Cerone, S. S. Dragomir, J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications , Demonstratio Math., 32 (1999), 697–712.

• [4] P. Cerone, S. S. Dragomir, J. Roumeliotis, J. Sunde , A new generalization of the trapezoid formula for n-time differentiable mappings and applications, Demonstratio Math., 33 (2000), 719–736.

• [5] S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, Victoria University, Australia (2000)

• [6] D.-Y. Hwang , Some Inequalities for n-time Differentiable Mappings and Applications, Kyungpook Math. J., 43 (2003), 335–343.

• [7] İ. İşcan , Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (2014), 935–942.

• [8] İ. İşcan, Ostrowski type inequalities for p-convex functions, New Trends Math. Sci., 4 (2016), 140–150.

• [9] İ. İşcan, M. Kunt , Hermite-Hadamard-Fejer type inequalities for harmonically quasi-convex functions via fractional integrals, Kyungpook Math. J., 56 (2016), 845–859.

• [10] İ. İşcan, M. Kunt , Hermite-Hadamard-Fejer type inequalities for quasi-geometrically convex functions via fractional integrals, J. Math., 2016 (2016), 7 pages.

• [11] İ. İşcan, S. Turhan , Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral, Moroccan J. Pure Appl. Anal., 2 (2016), 34–46.

• [12] İ. İşcan, S. Turhan, S. Maden, Some Hermite-Hadamard-Fejer type inequalities for Harmonically convex functions via Fractional Integral , New Trends Math. Sci., 4 (2016), 1–10.

• [13] W.-D. Jiang, D.-W. Niu, Y. Hua, 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.

• [14] U. S. Kirmaci, M. K. Bakula, M. E. Özdemir, J. Pečarić, Hadamard-type inequalities for s-convex functions, Appl. Math. Comp., 193 (2007), 26–35.

• [15] M. E. Özdemir, Ç. Yıldız, New Inequalities for Hermite-Hadamard and Simpson Type with Applications, Tamkang J. Math., 44 (2013), 209–216.

• [16] J. E. Pečarić, F. Porschan, Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, Boston (1992)

• [17] S.-H. Wang, B.-Y. Xi, F. Qi , Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex, Analysis (Munich), 32 (2012), 247–262.

• [18] B.-Y. Xi, F. Qi , Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means , J. Funct. Spaces Appl., 2012 (2012), 14 pages.

• [19] Ç. Yıldız, New inequalities of the Hermite-Hadamard type for n-time differentiable functions which are quasiconvex , J. Math. Inequal., 10 (2016), 703–711.