Related papers: A note on Hardy $q$-inequalities
We obtain simple proofs of certain inequalites for bivariate means.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
This a very brief account of the main line of development of Hardy inequalities.
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.
A refinement of the Hardy inequality has been presented by use of superquadratic function.
In this note we prove a weighted version of the Khintchine inequalities.
We give a direct proof of fractional Hardy inequality by means of Littlewood-Paley decomposition and properties of singular homogeneous kernels of degree -$d$. A refinement when $q>2$ is proved.
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…
We prove some extensions of Andrews inequality.
In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.
We extend a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality.
We prove some symmetric $q$-congruences.
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range $1<p\leq q<\infty.$ We also calculate the precise value of…
We give a simple proof of Hardy's inequality, based on the logarithmic Caccioppoli estimate for p-superharmonic functions in several variables.
The purpose of the paper is to present an short proof of the Chuang's inequality.
We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.