Refinements of Hermite-Hadamard inequality for operator convex function

Volume 10, Issue 11, pp 6035--6041 http://dx.doi.org/10.22436/jnsa.010.11.38

Publication Date: November 26, 2017 Submission Date: January 05, 2017

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Authors

Junmin Han - School of Mathematics and Information Science, Weifang University, Weifang, 261061, P. R. China. Jian Shi - College of Mathematics and Information Science, Hebei University, Baoding, 071002, P. R. China.

Abstract

In this paper, we present several operator versions of the Hermite-Hadamard inequality for the operator convex function, which are refinements of some operator convex inequalities presented by Dragomir [S. S. Dragomir, Appl. Math. Comput., \({\bf 218}\) (2011), 766--772] and [S. S. Dragomir, RGMIA Research Report Collection, \({\bf 2016}\) (2016), 15 pages].

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Keywords

• Self-adjoint operators
• Hermite-Hadamard inequality
• operator convex functions

References

• [1] V. Bacak, R. Türkmen, Refinements of Hermite-Hadamard type inequalities for operator convex functions, J. Inequal. Appl., 2013 (2013), 10 pages.
  • View Article
  • MathSciNet
  • MATH


• [2] N. S. Barnett, P. Cerone, S. S. Dragomir, Some new inequalities for Hermite-Hadamard divergence in information theory, Stochastic analysis and applications, Stoch. Anal. Appl., 3 (2002), 7–19.
  • MathSciNet
  • Google Scholar


• [3] A. Burqan , Improved Cauchy-Schwarz norm inequality for operators, J. Math. Inequal., 10 (2016), 205–211.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] S. S. Dragomir, Hermite-Hadamard type inequalities for operator convex functions, Appl. Math. Comput., 218 (2011), 766–772.
  • View Article
  • Google Scholar


• [5] S. S. Dragomir, Some Hermite-Hadamard Type Inequalities for Operator Convex Functions and Positive Maps, RGMIA Research Report Collection, 2016 (2016), 15 pages.
  • Google Scholar


• [6] S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities, RGMIA Monographs, Victoria University (2000)
  • Google Scholar


• [7] Y. Feng, Refinements of the Heinz inequalities, J. Inequal. Appl., 2012 (2012), 6 pages.


• [8] A. G. Ghazanfari, A. Barani, Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions, Banach J. Math. Anal., 9 (2015), 9–20.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] J. Hadamard, Étude sur les propriétés des fonctions entiéres et en particulier d’une fonction considérée par Riemann, (French), J. Math. Pures Appl., 58 (1893), 171–216.
  • Google Scholar
  • MATH


• [10] D. S. Mitrinović, I. B. Lacković, Hermite and convexity , Aequationes Math., 28 (1985), 229–232.
  • View Article
  • Google Scholar


• [11] M. S. Moslehian, Matrix Hermite-Hadamard type inequalities, Houston J. Math., 39 (2013), 177–189.
  • MathSciNet
  • Google Scholar


• [12] C. P. Niculescu, L.-E. Persson, Convex functions and their applications: A contemporary approach, Springer, New York (2006)
  • Google Scholar