On the stability of some positive linear operators from approximation theory

Recently, Popa and Raşa have shown the stability/ instability of some classical operators defined on [ 0 , 1 ] and obtained the best constant when the positive linear operators are stable in the sense of Hyers–Ulam. In this paper we show that the Kantorovich–Stancu type operators, King’s operator, B...

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Vydáno v:	Bulletin of mathematical sciences Ročník 5; číslo 2; s. 147 - 157
Hlavní autoři:	Mursaleen, M., Ansari, Khursheed J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel Springer Basel 01.07.2015 World Scientific Publishing Co. Pte., Ltd
Témata:	Mathematics Mathematics and Statistics 41A44 Kantorovich–Bernstein–Stancu type operator Szász–Mirakjan type operator Primary 39B82 Kantorovich–Stancu type operator Kantorovich–Szász–Mirakjan type operator Best constant King’s operator Secondary 41A35 Hyers–Ulam stability
ISSN:	1664-3607, 1664-3615
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Shrnutí:	Recently, Popa and Raşa have shown the stability/ instability of some classical operators defined on [ 0 , 1 ] and obtained the best constant when the positive linear operators are stable in the sense of Hyers–Ulam. In this paper we show that the Kantorovich–Stancu type operators, King’s operator, Bernstein–Stancu type operators, and Kantorovich–Bernstein–Stancu type operators with shifted knots are Hyers–Ulam stable. Further we find the best Hyers–Ulam stability constants for some of these operators. We also prove that Szász–Mirakjan and Kantorovich–Szász–Mirakjan type operators are unstable in the sense of Hyers and Ulam.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	1664-3607 1664-3615
DOI:	10.1007/s13373-015-0064-z