Geodesic
Iterates of (α, q)−Bernstein operators
Filomat, Tome 37 (2023) no. 22, p. 7663

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DOI

In this paper, the iterates of (α, q)-Bernstein operators are considered. Given fixed n ∈ N and q > 0, it is shown that for f ∈ C[0, 1] the k-th iterate T k n,q,α (f ; x) converges uniformly on [0, 1] to the linear function L f (x) passing through the points (0, f (0)) and (1, f (1)). Moreover, it is proved that, when q ∈ (0, 1), the iterates T jn n,q,α (f ; x), in which {j n } → ∞ as n → ∞, also converge to L f (x). Further, when q ∈ (1, ∞) and { j n } is a sequence of positive integers such that j n /[n] q → t as n → ∞, where 0 ≤ t ≤ ∞, the convergence of the iterates T jn n,q,α (p; x) for p being a polynomial is studied.
DOI : 10.2298/FIL2322663K
Classification : 47A75, 47B38
Keywords: q-calculus, Iterates, (α, q)-Bernstein polynomials, Uniform convergence 
Bülent Köroğlu; Fatma Taşdelen Yeşildal. Iterates of (α, q)−Bernstein operators. Filomat, Tome 37 (2023) no. 22, p. 7663 . doi: 10.2298/FIL2322663K
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     title = {Iterates of (\ensuremath{\alpha}, {q)\ensuremath{-}Bernstein} operators},
     journal = {Filomat},
     pages = {7663 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322663K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322663K/}
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