Approximation Properties for Modified Bernstein Operators on Simplex

Bernstein approximation is a kind of classic and abundant research subjects in the theory of approximations, which makes use of good properties and graceful structures of Bernstein polynomials to discuss a great deal of relations between Bernstein operators and the functions approached by it. In this paper, we transform the Bernstein polynomials on simplex of high dimension by decreasing the items of polynomials to get better calculation result. Two models of modified Bernstein operators are obtained and a new class of function is defined. By using the methods of function structure, the properties of inequality and Bernstein operators on simplex, the convergence of modified operators is investigated. An exact condition to insure the operators to converge with the smallest terms is also obtained.