On the images of entire functions under the limit q-Bernstein operator

Abstract

The limit q-Bernstein operator Bq comes out naturally as the limit for the sequence of q-Bernstein operators in the case 0 < q < 1. Alternatively, it can be viewed as a modification of the Szasz-Mirakyan operator related to the Euler distribution. In this paper, a necessary and sufficient condition for a function g to be an image of an entire function under Bq is presented.