Representations of two parameter quantum algebras and p,q-special functions

By Vivek Sahai, Sarasvati Yadav. 2007

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Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers (2015, unknown): “ot a replacement of q by q p . By some simple calculation, we have the following relation qk[n −k +1] p,q = [n+1]p,q −p n−k+1[k] p,q. For details on q-calculus and (p,q)-calculus, one can refer [15], [5, 12, 13], respectively. Now based on (p,q)-integers, we construct (p,q)-analogue of BBH-operators”
(p,q)‐Generalization of Szász–Mirakyan operators (2015, background): “d that f is diﬀerentiable at 0. The formula for the (p,q)-derivative of a product is Dp,q (u(x)v(x)) := Dp,q (u(x))v(qx) +Dp,q (v(x))u(qx). For more details on (p,q)-calculus, we refer the readers to [5, 8, 7, 14, 15] and references therein. There are two (p,q)-analogues of the exponential function,”
(p, q)-Beta functions and applications in approximation (2016, background): “etc]. The further generalization of quantum calculus is the post-quantum calculus, denoted by (p,q)-calculus. Recently, some researchers started working in this direction (see e.g [13], [2], [10] and [16] etc.). Some basic deﬁnitions and theorems, which are mentioned below may be found in these pape”
BERNSTEIN DURRMEYER OPERATORS BASED ON TWO PARAMETERS (2016, background): “For (p, q)-calculus, we mention here some basic definitions and theorems, some of them may be found in the recent papers [7], [10], [8], [11] etc.”