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.
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.
2 Auxiliary lemmas
Firstly, we prove (2.13) by considering the following two cases.
It can be proved in a way similar to Lemma 6. □
3 Proofs of theorems
3.1 Proof of Theorem 1
3.2 Proof of Theorem 2
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