Research Article
BibTex RIS Cite

Year 2017, Volume: 13 Issue: 2, 353 - 358, 30.06.2017

Merve Avcı Ardıç Emin Özdemir

https://doi.org/10.18466/cbayarfbe.319873

Abstract

References

  • [1] Alomari, M; Darus M. On the Hadamard’s inequality for convex functions on the coordinates, Journal of Inequalities and Applications, Volume 2009, Article ID 283147, 13 pages. http://192.43.228.178/journals/HOA/JIA/Volume2009/283147.pdf
  • [2] Dragomir, SS. Some Jensen’s Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces, Bulletin of the Malaysian Mathematical Sciences Society, 2011, 34 /3: 445-454. https://www.emis.de/journals/BMMSS/pdf/v34n3/v34n3p3.pdf
  • [3] Niculescu, CP. The Hermite–Hadamard inequality for convex functions, Nonlinear Analysis, 2012, 75: 662–669.
  • [4] Pachpatte, B. G. A note on integral inequalities involving two log-convex functions, Mathematical Inequalities & Applications, 2004, 7/4: 511–515.
  • [5] Pečarić, J; Rehman, A. U. On logarithmic convexity for power sums and related results, Journal of Inequalities and Applications, vol. 2008, Article ID 389410, 9 pages, 2008. https://www.emis.de/journals/HOA/JIA/Volume2008/305623.pdf
  • [6] Yang, G. S.; Tseng, KL, Wang H. T. A note on integral inequalities of Hadamard type for convex and concave functions, Taiwanese Journal of Mathematics, 2012, 16 /2: 479-496. http://society.math.ntu.edu.tw/~journal/tjm/V16N2/TJM-273.pdf
  • [7] Zhanga, X; Jiang, W. Some properties of convex function and applications for the exponential function, Computers and Mathematics with Applications, 2012, 63: 1111–1116. http://fulltext.study/preview/pdf/471578.pdf
  • [8] Shuang, Y; Wang, Y; Qi, F. Some inequalities of Hermite-Hadamard type for functions whose third derivatives are convex, Journal of Computational Analysis and Applications, 2014, 17/2: 272-279.

Inequalities for log-convex functions via three times differentiability

Year 2017, Volume: 13 Issue: 2, 353 - 358, 30.06.2017

Merve Avcı Ardıç Emin Özdemir

https://doi.org/10.18466/cbayarfbe.319873

Abstract


In
this paper, some new integral inequalities like Hermite-Hadamard type for functions
whose third derivatives absolute value are convex are established. Some applications to quadrature formula
for midpoint error estimate are given.





Keywords

Convexity log-convex functions Hermite-Hadamard inequality Hölder integral inequality Power-mean integral inequality

References

  • [1] Alomari, M; Darus M. On the Hadamard’s inequality for convex functions on the coordinates, Journal of Inequalities and Applications, Volume 2009, Article ID 283147, 13 pages. http://192.43.228.178/journals/HOA/JIA/Volume2009/283147.pdf
  • [2] Dragomir, SS. Some Jensen’s Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces, Bulletin of the Malaysian Mathematical Sciences Society, 2011, 34 /3: 445-454. https://www.emis.de/journals/BMMSS/pdf/v34n3/v34n3p3.pdf
  • [3] Niculescu, CP. The Hermite–Hadamard inequality for convex functions, Nonlinear Analysis, 2012, 75: 662–669.
  • [4] Pachpatte, B. G. A note on integral inequalities involving two log-convex functions, Mathematical Inequalities & Applications, 2004, 7/4: 511–515.
  • [5] Pečarić, J; Rehman, A. U. On logarithmic convexity for power sums and related results, Journal of Inequalities and Applications, vol. 2008, Article ID 389410, 9 pages, 2008. https://www.emis.de/journals/HOA/JIA/Volume2008/305623.pdf
  • [6] Yang, G. S.; Tseng, KL, Wang H. T. A note on integral inequalities of Hadamard type for convex and concave functions, Taiwanese Journal of Mathematics, 2012, 16 /2: 479-496. http://society.math.ntu.edu.tw/~journal/tjm/V16N2/TJM-273.pdf
  • [7] Zhanga, X; Jiang, W. Some properties of convex function and applications for the exponential function, Computers and Mathematics with Applications, 2012, 63: 1111–1116. http://fulltext.study/preview/pdf/471578.pdf
  • [8] Shuang, Y; Wang, Y; Qi, F. Some inequalities of Hermite-Hadamard type for functions whose third derivatives are convex, Journal of Computational Analysis and Applications, 2014, 17/2: 272-279.
There are 8 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Merve Avcı Ardıç This is me

Emin Özdemir

Publication Date June 30, 2017
Published in Issue Year 2017 Volume: 13 Issue: 2

Cite

APA Avcı Ardıç, M., & Özdemir, E. (2017). Inequalities for log-convex functions via three times differentiability. Celal Bayar University Journal of Science, 13(2), 353-358. https://doi.org/10.18466/cbayarfbe.319873
AMA Avcı Ardıç M, Özdemir E. Inequalities for log-convex functions via three times differentiability. CBUJOS. June 2017;13(2):353-358. doi:10.18466/cbayarfbe.319873
Chicago Avcı Ardıç, Merve, and Emin Özdemir. “Inequalities for Log-Convex Functions via Three Times Differentiability”. Celal Bayar University Journal of Science 13, no. 2 (June 2017): 353-58. https://doi.org/10.18466/cbayarfbe.319873.
EndNote Avcı Ardıç M, Özdemir E (June 1, 2017) Inequalities for log-convex functions via three times differentiability. Celal Bayar University Journal of Science 13 2 353–358.
IEEE M. Avcı Ardıç and E. Özdemir, “Inequalities for log-convex functions via three times differentiability”, CBUJOS, vol. 13, no. 2, pp. 353–358, 2017, doi: 10.18466/cbayarfbe.319873.
ISNAD Avcı Ardıç, Merve - Özdemir, Emin. “Inequalities for Log-Convex Functions via Three Times Differentiability”. Celal Bayar University Journal of Science 13/2 (June 2017), 353-358. https://doi.org/10.18466/cbayarfbe.319873.
JAMA Avcı Ardıç M, Özdemir E. Inequalities for log-convex functions via three times differentiability. CBUJOS. 2017;13:353–358.
MLA Avcı Ardıç, Merve and Emin Özdemir. “Inequalities for Log-Convex Functions via Three Times Differentiability”. Celal Bayar University Journal of Science, vol. 13, no. 2, 2017, pp. 353-8, doi:10.18466/cbayarfbe.319873.
Vancouver Avcı Ardıç M, Özdemir E. Inequalities for log-convex functions via three times differentiability. CBUJOS. 2017;13(2):353-8.