On the generalized Boolean sum Schurer-Stancu approximation formula

Abstract

. In this paper, the Schurer-Stancu generalized Boolean sum (GBS, for short) approximation formula is considered and it’s remainder term is expressed in terms of bivariate divided differences. When the approximated function is sufficiently smooth, an upper bound estimation for the remainder term is also established. As particular cases, GBS Schurer and respectively GBS Bernstein approximation formulas are obtained and the expressions of their remainder are explicitly given.