On Pointwise Convergence of q-Bernstein Operators and Their q-Derivatives

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q‐Voronovskaya type theorems for q‐Baskakov operators (2016, methodology): “In the paper [13], we achieved to obtain quantitative Voronovskaya theorem for q-Bernstein polynomials and their q -derivatives with the second q-derivative of approximating function, which allows us to present Voronovskaya type theorem for continuous function at any point x 2 .”
Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators (2016, background): “Then, the inequality !!!!!!![n]qn [Sn,qn (f ; x) − f(x)] − (x2(1 − qnn)/qn + x)D2qn f(x) [2]qn !!!!!!! ≤ O(1)Ω(D2qn f ; [n]−1/2 qn ) holds for any x ∈ [0,∞).”
Blending type approximation by generalized Bernstein-Durrmeyer type operators (2018, background): “Among other papers, we refer the readers to [3, 7, 9, 13, 23, 25].”