Quantitative inheritance properties for simultaneous approximation by tensor product operators II: Applications

We summarize several general results concerning quantitative inheritance properties for simultaneous approximation by tensor product operators and apply these to various situations. All inequalities are given in terms of moduli of continuity of higher order

Evaluarea ordinului de aproximare prin operatori liniari si pozitivi

Auswertung der Approximationsgüte durch positive lineare Operatoren Abstract: The areas of research covered by this thesis can be roughly divided into three parts: aspects of quantitative approximation, studying of shape-preservation properties and over-iteration for some selected operators. Regarding the quantitative approximation we study traditional problems like: direct estimates, degree of simultaneous approximation or global smoothness preservation (Chapters 2, 3). On the other hand, we also present some non-classical issues like: estimates for the Peano remainder, a quantitative Voronovskaja theorem or estimates for differences of two positive linear operators (Chapter 5). Our object of study are different classes of operators: rational type operators, composite Beta type operators, but also other types that cannot be classified like: the BLaC-wavelet operator and the King operator