On Approximation by Max-product Shepard Operators

In the present paper, we firstly give Jackson type estimates of approximation by max-product Shepard operators on [ - 1 , 1 ] , which combine pointwise and global estimates as a whole. Secondly, we investigate the weighted approximation by modified max-product Shepard operator for functions with singularities at the endpoints. Finally, we generalize max-product Shepard operators to the bounded convex set Ω on the scattered data, and obtain Jackson type estimates of approximation.