1. School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; 2. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
Abstract:
We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.