Research Article

Some new integral inequalities for n-times differentiable log-convex functions

Volume: 5 Number: 2 March 30, 2017
EN

Some new integral inequalities for n-times differentiable log-convex functions

Abstract

 In this work, by using an integral identity together with both the Ho¨lder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable log-convex functions.

Keywords

References

  1. [1] M. Alomari and M. Darus, “On The Hadamard’s Inequality for Log-Convex Functions on the Coordinates”, Hindawi Publishing Corporation Journal of Inequalities and Applications, Volume 2009, Article ID 283147, 13 pages, doi:10.1155/2009/283147.
  2. [2] M. A. Ardıc¸ and M. Emin ¨Ozdemir, “Inequalities for log-convex functions vıa three times differentiability”, arXiv:1405.7480v1 [math.CA] 29 May 2014.
  3. [3] S. P. Bai, S.-H. Wang and F. Qi, “Some Hermite-Hadamard type inequalities for n-time differentiable ( α ,m)-convex functions”, Jour. of Ineq. and Appl., 2012, 2012:267.
  4. [4] 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.
  5. [5] 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.
  6. [6] 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/hermite hadamard.html.
  7. [7] S.S. Dragomir, “New jensen’s type inequalities for differentiable log-convex functions of selfadjoint operators in Hilbert spaces”, Sarajevo Journal of Mathematics, Vol.7 (19) (2011), 67-80.
  8. [8] D. Y. Hwang, “Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335–343.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

İmdat Iscan * This is me
Türkiye

Huriye Kadakal This is me
Türkiye

Publication Date

March 30, 2017

Submission Date

January 2, 2017

Acceptance Date

March 4, 2017

Published in Issue

Year 2017 Volume: 5 Number: 2

APA
Iscan, İ., Kadakal, H., & Kadakal, M. (2017). Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences, 5(2), 10-15. https://izlik.org/JA43CZ55XU
AMA
1.Iscan İ, Kadakal H, Kadakal M. Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences. 2017;5(2):10-15. https://izlik.org/JA43CZ55XU
Chicago
Iscan, İmdat, Huriye Kadakal, and Mahir Kadakal. 2017. “Some New Integral Inequalities for N-Times Differentiable Log-Convex Functions”. New Trends in Mathematical Sciences 5 (2): 10-15. https://izlik.org/JA43CZ55XU.
EndNote
Iscan İ, Kadakal H, Kadakal M (March 1, 2017) Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences 5 2 10–15.
IEEE
[1]İ. Iscan, H. Kadakal, and M. Kadakal, “Some new integral inequalities for n-times differentiable log-convex functions”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 10–15, Mar. 2017, [Online]. Available: https://izlik.org/JA43CZ55XU
ISNAD
Iscan, İmdat - Kadakal, Huriye - Kadakal, Mahir. “Some New Integral Inequalities for N-Times Differentiable Log-Convex Functions”. New Trends in Mathematical Sciences 5/2 (March 1, 2017): 10-15. https://izlik.org/JA43CZ55XU.
JAMA
1.Iscan İ, Kadakal H, Kadakal M. Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences. 2017;5:10–15.
MLA
Iscan, İmdat, et al. “Some New Integral Inequalities for N-Times Differentiable Log-Convex Functions”. New Trends in Mathematical Sciences, vol. 5, no. 2, Mar. 2017, pp. 10-15, https://izlik.org/JA43CZ55XU.
Vancouver
1.İmdat Iscan, Huriye Kadakal, Mahir Kadakal. Some new integral inequalities for n-times differentiable log-convex functions. New Trends in Mathematical Sciences [Internet]. 2017 Mar. 1;5(2):10-5. Available from: https://izlik.org/JA43CZ55XU