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2 2018

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Quantitative approximation by shift invariant multivariate sublinear-Choquet operators

Anastassiou G. A.

Journal of Applied Analysis

2018

Vol. 24, nr 2

115--126

A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it, sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized operators are presented fulfilling all the above properties; the higher order of multivariate approximation of these operators is also studied.

Approximations by multivariate sublinear and Max-product operators under convexity

Anastassiou G. A.

Demonstratio Mathematica

2018

Vol. 51, nr 1

85--105

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.