Related papers: q-Bernoulli Inequality

A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.

In this paper, we use two different approaches to introduce $q$-analogs of Riemann's zeta function and prove that their values at even integers are related to the $q$-Bernoulli and $q$ Euler's numbers introduced by Ismail and Mansour…

We prove Burkholder inequality using Bregman divergence.

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.

In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.

I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…

In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

In this paper we establish a $q$-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.

We prove some symmetric $q$-congruences.

We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…

In the present article, we have given a corrigendum to our paper ``On (p,q)-analogue of Bernstein operators" published in Applied Mathematics and Computation 266 (2015) 874-882.

In this, paper we obtain a q-analogue of a double inequality involving the Euler gamma function which was first proved geometrically by Alsina and Tomas and then analytically by Sandor

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted…

Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of…

In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.

We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.

We prove a q-analogue of the formula $ \sum_{1\le k\le n} \binom nk(-1)^{k-1}\sum_{1\le i_1\le i_2\le... \le i_m=k}\frac1{i_1i_2... i_m} = \sum_{1\le k\le n}\frac{1}{k^m} $ by inverting a formula due to Dilcher.