Related papers: q-Bernoulli Inequality
In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.
An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).
In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.
\footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality…
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
The summary of the Author's results on Bell inequalities and macroscopic entanglement.
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The violation of Bell's inequality is explained by maintaining realism, inductive inference and Einstein separability.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
Using the methodology of (rigorous) {\it experimental mathematics}, we give a simple and motivated solution to Zudilin's question concerning a $q$-analog of a problem posed by Asmus Schmidt about a certain binomial coefficients sum. Our…
Interpretations for the q-binomial coefficient evaluated at -q are discussed. A (q,t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces.
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.
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…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
Let $q \in (0,1)$. We formulate an asymptotic version of the $q$-analogue of de Finetti's theorem. Using the convex structure of the space of $q$-exchangeable probability measures, we show that the optimal rate of convergence is of order…