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On a q-analogue of Stancu operators

Octavian Agratini (2010)

Open Mathematics

This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for the rate of convergence. A probabilistic approach is presented and approximation properties are established.

On a Theorem of Ingham.

S. Jaffard, M. Tucsnak, E. Zuazua (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On an Extremal Problem concerning Bernstein Operators

Gonska, Heinz, Zhou, Ding-Xuan (1995)

Serdica Mathematical Journal

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.The best constant problem for Bernstein operators with respect to the second modulus of smoothness is considered. We show that for any 1/2 ≤ a < 1, there is an N(a) ∈ N such that for n ≥ N(a), 1−a≤k, n≤a, sup | Bn (f, k/n) − f(k/n) | ≤ cω2(f, 1/√n), where c is a constant,0 < c < 1.

On approximation by Chebyshevian box splines

Zygmunt Wronicz (2002)

Annales Polonici Mathematici

Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions w j are of the form w j ( x ) = W j ( v n + j · x ) , where the functions W j are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.

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