Related papers: New inequalities for the generalized Karcher mean
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to…
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting…
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…
Loewner partial order plays a very important role in metric topology and operator inequality on the open convex cone of positive invertible operators. In this paper we consider a family G of the ordered means for positive invertible…
Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular,…
If $\sigma$ is a symmetric mean and $f$ is an operator monotone function on $[0, \infty)$, then $$f(2(A^{-1}+B^{-1})^{-1})\le f(A\sigma B)\le f((A+B)/2).$$ Conversely, Ando and Hiai showed that if $f$ is a function that satisfies either one…
Some real functions f induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define linear mapping beta on matrices (which is basic in the…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities then can be applied to a wide class of special functions…
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference…
This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…
Let $C$ be an open cone in a Banach space equipped with the Thompson metric with closure a normal cone. The main result gives sufficient conditions for Borel probability measures $\mu,\nu$ on $C$ with finite first moment for which $\mu\leq…
We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.
Non-asymptotic statistical analysis is often missing for modern geometry-aware machine learning algorithms due to the possibly intricate non-linear manifold structure. This paper studies an intrinsic mean model on the manifold of restricted…
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…