Related papers: On (p,q)-analogue of Bernstein Operators (Revised)
In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.
We introduce a $q$-analog of the polyanalytic Bargmann transform on $\mathbb{C}$.
Rejoinder to ``Equi-energy sampler with applications in statistical inference and statistical mechanics'' by Kou, Zhou and Wong [math.ST/0507080]
In this paper, the divisibility property of the type 2 $(p, q)$-analogue of the $r$-Whitney numbers of the second kind is established. More precisely, a congruence relation modulo $pq$ for this $(p,q)$-analogue is derived.
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity…
Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…
Nonlinear q-Bernstein operator of max-product kind was introduced and its approximation order was examined, and the order of approximation was found to be by Duman in. In this paper, we obtained a better order of approximation for this…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein…
We give an overview about the power product expansion of the exponential series and derive some q-analogs
The aim of this article is to introduce a bivariate extension of Shurer-Stancu operators based on (p q)integers. We prove uniform approximation by means of Bohman Korovkin type theorem rate of convergence using total modulus of smoothness…
Correction to The Annals of Statistics (1989) 17 1749--1766 [URL: http://links.jstor.org/sici?sici=0090-5364%28198912%2917%3A4%3C1749%3AEPEFSP%3E 2.0.CO%3B2-9]
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
In this revised version, we add some expository material and references and make some minor corrections.
Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev. D 40, (1989) 315] are corrected.
In this paper, we make some remarks on Jos\'e Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…