- Open Access
Pointwise approximation by a Durrmeyer variant of Bernstein-Stancu operators
© The Author(s) 2017
- Received: 19 August 2016
- Accepted: 27 December 2016
- Published: 27 January 2017
In the present paper, we introduce a kind of Durrmeyer variant of Bernstein-Stancu operators, and we obtain the direct and converse results of approximation by the operators.
- Bernstein-Stancu type operators
- pointwise and global estimates
- inverse results
Our first result can be read as follows.
Throughout the paper, C denotes either a positive absolute constant or a positive constant that may depend on some parameters but not on f, x, and n. Their values may be different at different locations.
For the converse result, we have the following.
Firstly, we prove (2.13) by considering the following two cases.
It can be proved in a way similar to Lemma 6. □
3.1 Proof of Theorem 1
3.2 Proof of Theorem 2
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