相关论文: On the H\"older and Cauchy--Schwarz inequalities
We present some identities related to the Cauchy-Schwarz inequality in complex inner product spaces. A new proof of the basic result on the subject of Strengthened Cauchy-Schwarz inequalities is derived using these identities. Also, an…
We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq…
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
In this article we discuss a generalized Wirtinger inequality.
We establish in this note some Cauchy-Schwarz-type inequalities on compact K\"{a}hler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higher-dimensional cases. Our proof is to make full use of the mixed…
Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.
We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy-Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in…
In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.
In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical…
In this article, we establish an improvement of the Cauchy-Schwarz inequality. Let $x, y \in \mathcal{H},$ and let $f: (0,1) \rightarrow \mathbb{R}^+$ be a well-defined function, where $\mathbb{R}^+$ denote the set of all positive real…
The aim of this paper is to present necessary and sufficient conditions for generalized H\"{o}lder's inequality on generalized Morrey spaces. We also obtain similar results on weak Morrey spaces and on generalized weak Morrey spaces. The…
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference…
The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.
In this survey we consider generalizations for Young and Cauchy--Bunyakowsky inequalities with applications.
We obtain some inequalities which are stronger than the Schur majorization inequalities.
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).