Related papers: q-Bernoulli Inequality

We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.

In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.

We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.

In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.

We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…

The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even, $t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$, where $a$ and $b$ are…

This paper investigates $q$-analogues of the classical Bernoulli polynomials and numbers. We introduce a new polynomial sequence ${\left(B_{n , q}(X)\right)}_{n \in \mathbb{N}_0}$, defined via the Jackson integral, and explore its…

We prove a Lucas-type congruence for q-Delannoy numbers.

We provide a $q$-analogue of Euler's formula for $\zeta(2k)$ for $k\in\mathbb{Z}^+$. Our main results are stated in Theorems 3.1 and 3.2 below. The result generalizes a recent result of Z.W. Sun who obtained $q$-analogues of…

In this paper, we investigate a specific class of $q$-polynomial sequences that serve as a $q$-analogue of the classical Appell sequences. This framework offers an elegant approach to revisiting classical results by Carlitz and, more…

Equivalencies of many basic elementary inequalities are given

We study the twisted q-zeta functions and twisted q-Bernoulli polynomials

In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

In this article, we propose a q-analogue of the Drinfeld-Sokolov hierarchy of type A. We also discuss its relationship with the q-Painleve VI equation and the q-hypergeometric function.

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

We prove some integral inequalities related to Feng Qi's inequality (2000) and obtain a few corollaries.