Kamel Brahim

Asymptotic Approximations in Quantum Calculus

Abstract This paper aims to study the asymptotic approximation of some functions defined by the q-Jackson integrals, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical methods by giving their q-analogues. In particular, a q-analogue of the Watson’s lemma is discussed and new asymptotic expansions of the q−j α Bessel function and of the q-complementary error function are established.

Some inequalities for the q-beta and the q-gamma functions via some q-integral inequalities

Some new inequalities for the q-gamma, the q-beta and the q-analogue of the Psi functions are established via some q-integral inequalities.

Tauberian Theorems In Quantum Calculus

Abstract In this paper we attempt to establish some tauberian theorems in quantum calculus. This constitutes the beginning of the study of the q-analogue of analytic theory of numbers which is the aim of a forthcoming paper.

Two dimensional Mellin transform in Quantum Calculus

Abstract In this article, we introduce the two dimensional Mellin transform M q ˜ ( f ) ( s , t ) , give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.

On q-Gamma and q-Bessel Functions

In this paper, we present some characterizations of the q-Gamma and the properties of the q-Bessel functions.