Related papers: A note on the Menchov-Rademacher Inequality
This paper refines the argument of Lehman by reducing the size of the constants in Turing's method. This improvement is given in Theorem 1 and scope for further improvements is also given. Analogous improvements to Dirichlet L-functions and…
We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known…
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…
The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
In this work we improve the sharp Hardy inequality in the case $p>n$ by adding an optimal weighted Hoelder semi-norm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for $p>n$…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
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…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
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 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.
We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the…