扰动Ostrowski型不等式的新推广及其应用

A generalization of Ostrowski inequality on time scales for k points

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.

A new generalization of Ostrowski type inequality on time scales

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral type inequalities on time scales as special cases.

New inequalities for n- time differntiable functions

In this paper, we obtain several inequalities of Ostrowski type that the absolute values of n-time differntiable functions are convex.

Korneichuk–Stechkin 引理、Ostrowski 与 Landau 不等式，以及 $L$-空间值函数的最优恢复问题

Korneichuk-Stechkin Lemma, Ostrowski and Landau inequalities, and optimal recovery problems for $L$-space Valued Functions

本文建立 $L$-空间值函数的 Korneichuk–Stechkin 引理，据此推出精确 Ostrowski 与 Landau 不等式，并统一解决多类算子、函数、导数及积分的最优恢复问题。

抽象距离空间中的 Ostrowski 型不等式

Ostrowski-type inequalities in abstract distance spaces

本文在取值于含最小元素偏序集的抽象距离与伪度量空间中，针对 Lipschitz 映射族建立了尖锐的 Ostrowski 型偏差不等式，并统一涵盖多种已知估计。

Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces

The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well. Generalizations of the Boas-Bellman, Bombieri, Selberg, Heilbronn and Pecaric inequalities for finite sequences of vectors that are not necessarily orthogonal are also provided. Two extensions of the celebrated Ostrowski's inequalities for sequences or real numbers and the generalization of Wagner's inequality in…

A treatment of the Cauchy--Schwarz inequality in $C^*$-modules

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra $\A$. The key idea is to consider a semi-inner product $\A$-module as a semi-inner product $\A$-module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy--Schwarz inequality. As a consequence, w…

Functions of perturbed unbounded self-adjoint operators. Operator Bernstein type inequalities

This is a continuation of our papers \cite{AP2} and \cite{AP3}. In those papers we obtained estimates for finite differences $(\D_Kf)(A)=f(A+K)-f(A)$ of the order 1 and $(\D_K^mf)(A)\df\sum\limits_{j=0}^m(-1)^{m-j}(m\j)f\big(A+jK\big)$ of the order $m$ for certain classes of functions $f$, where $A$ and $K$ are bounded self-adjoint operator. In this paper we extend results of \cite{AP2} and \cite{AP3} to the case of unbounded self-adjoint operators $A$. Moreover, we obtain operator Bernstein type inequalities for entire functions of exponential type. This allows us to obtain alternative proofs…

Quantitative bounds on the discrete spectrum of non self-adjoint quantum magnetic Hamiltonians

We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{ö}dinger and Pauli with constant magnetic field of strength $b\textgreater{}0$. In particular, we use these bounds to obtain some information on the distribution of the eigenvalues of the perturbed operators in the neighborhood of their essential spectrum.