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...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of mathematical sciences Vol. 5; no. 2; pp. 147 - 157
Main Authors: Mursaleen, M., Ansari, Khursheed J.
Format: Journal Article
Language:English
Published: Basel Springer Basel 01.07.2015
World Scientific Publishing Co. Pte., Ltd
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1664-3607
1664-3615
DOI:10.1007/s13373-015-0064-z