相关论文: Reverses of operator Acz\'el inequality
Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More…
Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.
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…
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…
In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.
It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…
We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities…
In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the H\"{o}lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical…
In this paper, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert…
We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain…
We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are…
The Riesz-Sobolev inequality relates the convolution of nonnegative functions on Euclidean space to the convolution of their symmetric nonincreasing rearrangements. We show that for dimension one, for indicator functions of sets, if the…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
In this paper, we first provide a better estimate of the second inequality in Hermite-Hadamard inequality. Next, we study the reverse of the celebrated Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for…
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…
We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric means of positive kernel operators on Banach function and sequence…
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
We present a Diaz--Metcalf type operator inequality as a reverse Cauchy-Schwarz inequality and then apply it to get the operator versions of P\'{o}lya-Szeg\"{o}'s, Greub-Rheinboldt's, Kantorovich's, Shisha-Mond's, Schweitzer's, Cassels' and…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.