Some New Karamata Type Inequalities and Their Applications to Some Entropies

@article{Furuichi2019SomeNK,
  title={Some New Karamata Type Inequalities and Their Applications to Some Entropies},
  author={Shigeru Furuichi and Hamid Reza Moradi and Akram Zardadi},
  journal={Reports on Mathematical Physics},
  year={2019}
}
7 Citations
INEQUALITIES RELATED TO BEREZIN NORM AND BEREZIN NUMBER OF OPERATORS
. The Berezin symbol (cid:101) A of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel k λ is defined by ˜ A ( λ ) = (cid:68) A (cid:98) k λ ,
A Note on Kantorovich and Ando Inequalities.
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial
More accurate numerical radius inequalities (I)
ABSTRACT In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and
Operator Jensen's Type Inequalities for Convex Functions
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex)
More about operator order preserving
It is well known that increasing functions do not preserve operator order in general; nor do decreasing functions reverse operator order. However, operator monotone increasing or operator monotone
On the Operator Jensen Inequality for Convex Functions.
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex)
On the Jensen’s inequality and its variants
The main purpose of this paper is to discuss operator Jensen inequality for convex functions, without appealing to operator convexity. Several variants of this inequality will be presented, and some

References

SHOWING 1-10 OF 17 REFERENCES
Inequalities for Relative Operator Entropies and Operator Means
The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by using the Hermite-Hadamard inequality. We obtain alternative bounds for the Tsallis relative
Fundamental properties of Tsallis relative entropy
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between
Mond-Pecaric Method in Operator Inequalities
In Chapter 1 a very brief and rapid review of some basic topics in Jensen's inequality for positive linear maps and Kantorovich inequality for several types are given. Some basic ideas and the
Inequalities: Theory of Majorization and Its Applications
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of
Elements of Information Theory
TLDR
The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Matrix trace inequalities on the Tsallis entropies
Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis.
A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps
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
...
...