Stability of some positive linear operators on compact disk

Abstract

Recently, Popa and Rasa [27, 28] have shown the (in)stability of some classical operators defined on [0, 1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam (in)stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.