Related papers: Some Operator Inequalities via Convexity
The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to…
We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young inequalities are also given. In addition, operator inequalities for normalized positive linear…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
In this paper, we introduce two notions of a relative operator $(\alpha, \beta)$-entropy and a Tsallis relative operator $(\alpha, \beta)$-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative…
Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The…
Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis…
New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary…
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis…
Tsallis relative operator entropy is defined as a parametric extension of the relative operator entropy. Some properties of the Tsallis relative operator entropy are investigated. Also some operator inequalities related to the Tsallis…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
We obtain operator concavity (convexity) of some functions of two or three variables by using perspectives of regular operator mappings of one or several variables. As an application, we obtain, for $ 0<p < 1,$ concavity, respectively…
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. In addtition, some matrix trace…
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
Some new inequalities of Karamata type are established with a convex function in this paper. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c. Applying…
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean,…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…