Abstract

In the present paper, We consider the generalised form of iterative combinations of positive linear operators with well-known Bernstein and Baskakov operators as its particular case. We have estimated the iterative operator's $r^{th} $ moment and found a recurrence relation between the central moments and their derivatives. We deduce the Voronovskaya type asymptotic formula and the relation between the error of a continuous function and its norm with restrictions on its higher derivatives.

Keywords: Bernstein operators; iterative operators; Voronovskaya type asymptotic formula; modulus of continuity.

MSC: 41A25, 41A36

DOI: 10.57016/MV-mNadsfda

Pages:  1--10