ON THE IMAGES OF ENTIRE FUNCTIONS UNDER THE LIMIT q-BERNSTEIN OPERATOR

Abstract

The limit q-Bernstein operator B-q 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 B-q is presented.