Some approximation properties of \(q\)-Chlodowsky operators. (English) Zbl 1128.33014
The \(q\)-Bernstein operators were introduced by G. M. Phillips [Ann. Numer. Math. 4, No. 1–4, 511–518 (1997; Zbl 0881.41008)]. In this paper, the authors introduce \(q\) analogue of Chlodowsky operators. These operators are linear and positive for \( 0 < q \leq 1.\) The authors establsih some convergence results using the Borovkin-Korovkin theorem. They dtermine the rates of convergence, using different methods and investigate the monotonicity property of \(q\)-Chlodowsky operators.
Reviewer: P. R. Parthasarathy (Karlsruhe)
MSC:
| 33D05 | \(q\)-gamma functions, \(q\)-beta functions and integrals |
| 33D45 | Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) |
Keywords:
\(q\)-Chlodowsky polynomials; rate of convergence; modulus of continuity; Peetre-\(K \)functional; Lipschitz spaceCitations:
Zbl 0881.41008References:
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| [4] | Phillips, G. M., Bernstein polynomials based on \(q\)-integers, in The heritage of P.L. Chebyshev: a Festschrift in honour of the 70th birthday of T.J. Rivlin, Ann. Numer. Math., 4, 511-518 (1997) · Zbl 0881.41008 |
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