Approximations by multivariate sublinear and Max-product operators under convexity

Abstract

Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators. These are of Bernstein type, of Favard-Szász-Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite-Fejér interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated which fulfills a convexity assumption.

Keywords

• multivariate positive sublinear operators
• multivariate Max-product operators
• multivariate modulus of continuity
• convexity
• 41A17
• 41A25
• 41A36
• 41A63