Bernstein type operators with a better approximation for some functions

In this paper we construct new operators of Bernstein type with a better approximation than the classical Bernstein operator for some classes of functions on the whole interval [0,1]. Convergence of these operators and their shape preserving properties are discussed. We determine the subintervals in [0,1] in which the approximation order of constructed operators is better than that of the Bernstein operator for an arbitrary continuous function on the inter val [0,1]. Finally, we present comparisons with other two Bernstein type operators. 2013 Elsevier Inc. All rights reserved.