Bivariate positive linear operators constructed by means of q-Lagrange polynomials

On some summability methods for a q-analogue of an integral type operator based on multivariate q-Lagrange polynomials

“…n]q n converges to 0 as n → ∞, it will also converge to 0 in the sense of power series method. Further β (r) n + 1 [2]q n [n]q n ≤ 2 for each n ∈ N, hence in view of (4.8), we have Again, using the definition (4.7) and Lemma 1, we obtain…”

“…It has been observe that the above operator (1.5) was also indepedently tackled by Mursaleen et al [14] but unfortunately the proposed definition was incorrect while Behar et al [2] extended the study of Erkuş-Duman to the bi-variate and GBS (Generalized Boolean Sum) cases.…”

Characterization of deferred type statistical convergence andP‐summability method for operators: Applications toq‐Lagrange–Hermite operator

“…In this row, for $$$ g\in C\left[0,1\right] $$$, Erkuş et al 44 have defined a sequence of LPO using multivariate Lagrange polynomials and studied its approximation behavior by means of statistical convergence method. Mursaleen et al 45 attempted to define a $$$ q $$$‐(basic) analogue of the operator defined in Erkuş et al, 44 while Baxhaku et al 46 proposed a slight modification in the attempted operator and extended the study to the bivariate and Generalized Boolean Sum (GBS) cases.…”

A new kind of Bi-variate $ \lambda $ -Bernstein-Kantorovich type operator with shifted knots and its associated GBS form

“…For some more related and recent works in this direction, we refer the reader to (cf. [5], [2], [13], [14], [16], [17], [15], [22], and [25] etc. ).…”