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Year 2017, , 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, , 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

Cite

APA Avcı Ardıç, M., & Özdemir, E. (2017). Inequalities for log-convex functions via three times differentiability. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 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 Üniversitesi Fen Bilimleri Dergisi 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 Üniversitesi Fen Bilimleri Dergisi 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 Üniversitesi Fen Bilimleri Dergisi 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 Üniversitesi Fen Bilimleri Dergisi, 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.