Related papers: q-Bernoulli Inequality
Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.
We give a q-analogue of Gauss' divisibility theorem
In this article we give a proof of a q-analogue of the celebrated four functions theorem. This analogue was conjectured by Bjorner and includes as special cases both the four functions theorem and also Bjorner's q-analogue of the FKG…
In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.
In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
In this paper we present several natural $q$-analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some relating analytical results and ask for combinatorial interpretations.
In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.
Carlitz has introduced q-analogues of the Bernoulli numbers around 1950. We obtain a representation of these q-Bernoulli numbers (and some shifted version) as moments of some orthogonal polynomials. This also gives factorisations of Hankel…
We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.
We establish a q-analogue of Wolstenholme's harmonic series congruence.
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…