Tayebe Laal Shateri
In this article, by using the fixed point method, we prove the generalized Hyers--Ulam stability of biderivations from an algebra to a modular space, associated to bi-additive s-functional inequalities.
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Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies.
This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an operator mean is also considered. Such inequalities include discrete inequalities as special cases. Moreover, some generalizations of an additive Gruss integral inequality for operators are obtained.
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some results relevant to the Heron mean are also considered.
In a 2019 paper, Barnard and Steinerberger show that for $f\in L^1(\mathbf{R})$, the following autocorrelation inequality holds: \begin{equation*} \min_{0 \leq t \leq 1} \int_\mathbf{R} f(x) f(x+t)\ \mathrm{d}x \ \leq\ 0.411 ||f||_{L^1}^2, \end{equation*} where the constant $0.411$ cannot be replaced by $0.37$. In addition to being interesting and important in their own right, inequalities such as these have applications in additive combinatorics where some problems, such as those of minimal difference basis, can be encapsulated by a convolution inequality similar to the above integral. Barnar…
In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following problems: (i) the problem of approximating a function of an unbounded self-adjoint operator by bounded operators, (ii) the problem of best approximation of a certain class of elements from a Hilbert spac…
We prove two new reverse Cauchy--Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy--Schwarz inequality due to G Polya and G. Szego.
A generic functional inequality and Riccati pairs: an alternative approach to Hardy-type inequalities
本文在黎曼流形上提出加性与乘性泛函不等式，引入Riccati对扩展Bessel对，通过求解Riccati型ODE简洁证明多种Hardy型不等式，并在Cartan-Hadamard流形上证明精确不确定性原理。
In this paper we solve the problem of approximating functionals $(φ(A)x, f)$ (where $φ(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $ψ(A)$ of the operator $A$. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate $|(φ(A)x, f)|$ with the help of $\| ψ(A)x\|$ and $\| x\|$. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H${\rm{\ddot{o}}}$rmander theorem on comparison of operators in…
Assume that $X$ is a non-empty set and $T$ and $S$ are real or complex mappings defined on the product $X \times X$. Additive and multiplicative Sincov's equations are: $$T(x,z) = T(x, y ) + T(y, z)$$ and $$S(x,z) = S(x, y ) \cdot S(y, z),$$ respectively. Both equations play important roles in many areas of mathematics. In the present paper we study related inequalities. We deal with functional inequality $$ G(x,z) \leq G(x, y ) \cdot G(y, z), \quad x , y, z \in X $$ and we assume that $X$ is a topological space and $G\colon X \times X \to \mathbb{R}$ is a continuous mapping. In some our state…
Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain orbits of matrices (under the action of the unitary group). In this paper, we show that Lidskii's inequalities actually describe all global minimizers of such functions and that local minimizers are also global minimizers. We use these results to obtain partial results related to local minimizers of generalized frame operator distances in the context of finite fr…
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