Abstract
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.
Highlights
The equation of homomorphism is stable if every “approximate” solution can be approximated by a solution of this equation
Popa and Rasa obtained [15] a result on Hyers–Ulam stability of the Bernstein–Schnabl operators using a new approach to the Fréchet functional equation, and in [16,17], they have shown thestability of some classical operators defined on [0, 1] and find best constant when the positive linear operators are stable in the sense of Hyers–Ulam
The aim of this paper is to show that Kantorovich–Stancu type operators, an operator introduced by J
Summary
The equation of homomorphism is stable if every “approximate” solution can be approximated by a solution of this equation. Popa and Rasa obtained [15] a result on Hyers–Ulam stability of the Bernstein–Schnabl operators using a new approach to the Fréchet functional equation, and in [16,17], they have shown the (in)stability of some classical operators defined on [0, 1] and find best constant when the positive linear operators are stable in the sense of Hyers–Ulam. Further we find the best Hyers–Ulam stability constants for some of these operators.
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