On some class of Bernstein – type operators which represent a generalization of standard Bernstein operators

In this paper we introduced a new family of L. P. O. ℬ ¯ m ˙ , r ^ which represent a generalization of Bernstein oper. for a continuous function on the interval [0,1] . Our goal is to study the approximation properties of this sequence and study the uniformly convergence of it on some continuous functions on a compact set [0,1]. We find a rate of this convergence using a modulus of continuity. Finally we establish a formula of a Voronoviskaja-type asymptotic formula on ℬ ¯ m ˙ , r ^ .