Related papers: A complement to the Chebyshev integral inequality
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
In this paper, sufficient conditions for the existence of trigonometric Hermite-Jacobi appro\-ximations of a system of functions that are sums of convergent Fourier series are found. Based on these results, sufficient conditions are…
In this article we discuss a generalized Wirtinger inequality.
We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of…
We give necessary and sufficient conditions for the P\'olya--Szeg\"o type inequality with variable exponent of summability.
We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.
Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard…
We obtain sufficient conditions for conservativity of minimal quantum dynamical semigroup by modifying and extending the method used in [Chebotarev and Fagnola, J. Funct. Anal. 153(1998), 382-404]. Our criterion for conservativity can be…
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
We obtain some inequalities which are stronger than the Schur majorization inequalities.
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces .
We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if…
We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein-Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we…
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
An algebraic $q$-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this…
A family of exact upper bounds interpolating between Chebyshev's and Cantelli's is presented.
We give necessary integral conditions and sufficient ones for the existence of a general concept of $\mu$-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform…
The main result of this paper provides six necessary and sufficient conditions under various regularity assumptions for a so-called Cauchy mean to be identical to a two-variable quasiarithmetic mean. One of these conditions says that a…
We generalize the classical Minkowski integral inequality to the form involving general Banach function norms.