On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer operators

A basic problem of ( p , q ) $(p,q)$ -Bernstein-type operators

“…A sequence of -analogue of Bernstein operators was first introduced by Mursaleen [6, 7]. Besides, -analogues of Szász-Mirakyan [8], Baskakov Kantorovich [9], Bleimann-Butzer-Hahn [10] and Kantorovich-type Bernstein-Stancu-Schurer [11] operators were also considered, see [12–15]. For further developments, one can also refer to [8, 16–18].…”

“…The convergence theorems for -analogue Bernstein-type operators were established in some recent papers (see [6], Theorem 3.1 (Remark 3.1), [7], Theorem 1, and further reading [10], Theorem 2.2, [14], Theorem 3.1, [12], Theorem 3, and [11], Remark 2.3, see also [9, 15]). For example, Mursaleen [7] gives the following.…”

Bivariate tensor product ( p , q ) $(p, q)$ -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

“…A sequence of -analogue of Bernstein operators was first introduced by Mursaleen [1, 2]. Besides, -analogues of Szász-Mirakyan operators [3], Baskakov-Kantorovich operators [4], Bleimann-Butzer-Hahn operators [5] and Kantorovich-type Bernstein-Stancu-Schurer operators [6] were also considered. For further developments, one can also refer to [7–12].…”

“…Motivated by all the above results, in 2016, Cai et al [6] introduced a new kind of Kantorovich-type Bernstein-Stancu-Schurer operators based on -integers as follows: where for , , , , and . They got some approximation properties, since convergence properties of bivariate operators are important in approximation theory, and it seems there has been no papers mentioning the bivariate forms of above operators (1).…”

On (p,q)-analogue of divided differences and Bernstein operators

“…They applied it first to construct the (p, q)-analogue of the classical Bernstein operators [18]. Most recently, the (p, q)-analogues of several operators and related approximation theorems has been studied extensively; see [1,2,3,4,7,10,11,12,16,17,21,22] and the references therein.…”