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We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
Earlier work introduced a method for obtaining indefinite $q$-integrals of $q$-special functions from the second-order linear $q$-difference equations that define them. In this paper, we reformulate the method in terms of $q$-Riccati…
Negabent functions were introduced as a generalization of bent functions, which have applications in coding theory and cryptography. In this paper, we have extended the notion of negabent functions to the functions defined from…
We briefly recall the main physical features of the parton distributions in the quantum statistical picture of the nucleon. Some predictions from a next-to-leading order QCD analysis are compared to recent experimental results.
The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the…
In this paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…
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 consider a new class of space, called $N(p, q, s)$-type spaces, in the unit ball $B$ of $C^n$. We study some basic properties, Hadamard gaps, Hadamard products, Random power series, Korenblum's inequality, Gleason's…
A quasisymmetric function is assigned to every double poset (that is, every finite set endowed with two partial orders) and any weight function on its ground set. This generalizes well-known objects such as monomial and fundamental…
We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n+1)-th order differential equation and give a simple method for…
Let $M$ and $N$ be fixed non-negative integer numbers and let $\pi_N$ be a polynomial of degree $N$. Suppose that $(P_n)_{n\geq0}$ and $(Q_n)_{n\geq0}$ are two orthogonal polynomial sequences such that %their derivatives of orders $k$ and…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…
We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the $q$-cosine transform and the spherical Radon transform. We show that positively…
Our aim in this paper, is to establish certain new integrals for the the (p,q)-Mathieu--power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of thus special function. Moreover, we…
In this paper, we present and prove some generalizations of some inequalities for the $p$-Gamma, $q$-Gamma and $k$-Gamma functions. Our approach makes use of the series representations of the psi, $p$-psi, $q$-psi and $k$-psi functions.
We present the calculation of the two-loop spin splitting functions $P_{ij}^{(1)}(x)\; (i,j = q,g)$ contributing to the next-to-leading order corrected spin structure function $g_1(x,Q^2)$. These splitting functions, which are presented in…
In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.