A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps

Authors

  • S. S. Dragomir Victoria University.

DOI:

https://doi.org/10.4067/S0716-09172017000100005

Keywords:

Operator convex functions, Convex functions, Power function, Logarithmic function, Exponential function.

Abstract

In this paper we show that the celebrated Davis-Choi-Jensen’s inequality for normalised positive linear maps can be extended in a weakened form for convex functions. A reverse inequality and applications for important instances of convex (concave) functions are also given.

Author Biography

S. S. Dragomir, Victoria University.

College of Engineering & Science.

References

[1] M. D. Choi, Positive linear maps on C*-algebras. Canad. J. Math. 24, pp. 520—529, (1972).

[2] S. S. Dragomir, Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces. J. Inequal. Appl., Art. ID 496821, 15, (2010).

[3] S. S. Dragomir, Operator Inequalities of the Jensen, Cebysev and Grüss Type. Springer Briefs in Mathematics. Springer, New York, xii+121 pp. ISBN: 978-1-4614-1520-6, (2012).

[4] S. S. Dragomir and N. M. Ionescu, Some converse of Jensen’s inequality and applications. Rev. Anal. Numér. Théor. Approx. 23, No. 1, pp. 71-78. MR:1325895 (96c:26012), (1994).

[5] C. A. McCarthy, cp, Israel J. Math., 5, pp. 249-271, (1967).

[6] B. Mond and J. Pecaric, Convex inequalities in Hilbert space, Houston J. Math., 19, pp. 405-420, (1993).

[7] J. Pecaric, T. Furuta, J. Micic Hot and Y. Seo, Mond- Pecaric Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, (2005).

Published

2017-04-06

How to Cite

[1]
S. S. Dragomir, “A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps”, Proyecciones (Antofagasta, On line), vol. 36, no. 1, pp. 81-94, Apr. 2017.

Issue

Section

Artículos