The generalized order and the generalized type of an entire function in terms of the best approximation

Abstract

The paper explores connection between the generalized order and the generalized type of an entire function and the speed of the best polynomial approximation in the unit disk. The relations which define the generalized order and the generalized type of an entire function through the sequence of its best approximations, have been found. The results were obtained by generalization previous results of A.R. Reddy, D. Sato, I.I. Ibragimov and N. I. Shyhaliev, S. B. Vakarchyk, R. Mamadov.