Abstract

Here we transfer basic real approximations to corresponding vectorial and fuzzy setting of: Bernstein polynomials, Bernstein-Durrmeyer operators, genuine Bernstein-Durrmeyer operators, Stancu type operators and special Stancu operators. These are convergences to the unit operator with rates. We also give the convergence with rates to zero of the difference of genuine Bernstein-Durrmeyer and special Stancu operators. All approximations involve Jackson type inequalities and moduli of smoothness of various orders. In order to transfer we develop basic and important general results at the vectorial and fuzzy level. Our technique goes from real to vectorial and then to fuzzy setting. This chapter is based on [58].

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