Related papers: Some Operator Inequalities via Convexity
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
We give a refined Young inequality which generalizes the inequality by Zou--Jiang. We also show the upper bound for the logarithmic mean by the use of the weighted geometric mean and the weighted arithmetic mean. Furthermore, we show some…
Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
The main goal of this article is to establish several new $\mathbb{A}$-numerical radius equalities and inequalities for $n\times n$ cross-diagonal, left circulant, skew left circulant operator matrices, where $\mathbb{A}$ is the $n\times n$…
For finite-dimensional operator systems $\mathcal{S}_{\mathsf T}$, ${\mathsf T} \in B({\mathcal H})^d$, we show that the local lifting property and $1$-exactness of $\mathcal{S}_{\mathsf T}$ may be characterized by measurements of the…
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via…
The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results.
The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative…
In this article, we employ certain properties of the transform $C_{M,m}(A)=(MI-A^*)(A-mI)$ to obtain new inequalities for the bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. In particular, we obtain new relations among…
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.
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
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…
We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…
We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We establish their basic properties and extend the operator inequalities on relative operator entropies and Tsallis…
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…
The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…