Direct and converse results for multivariate generalized Bernstein polynomials

In this paper, the following generalization of multivariate Bernstein polynomials has been studied:Bn(f;x1,x2,…,xm)=∑k1,k2,…,km=0nfk1bn,k2bn,…,kmbn∏j=1mnkjxjkj(1-xj)n-kj,where (bn)(bn) is a sequence of positive numbers such that limn→∞n/bn=1limn→∞n/bn=1 and direct and inverse theorems for this polynomials have been presented.