相关论文: On the Bombieri Inequality in Inner Product Spaces
We present an expository account of the Bushell-Okrasi\'nski inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in studies of nonlinear Volterra equations but very soon gained…
New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.
In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.
Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
Some sharp inequalities of Gruss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.
This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for…
The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…
In this paper some Tur\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\'anian of…
Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is…
In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Tur\'an type inequalities for…