Abstract
Recently, Popa and Rasa 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 Szasz-Mirakjan and Kantorovich-Szasz-Mirakjan type operators are unstable in the sense of Hyers and Ulam.