Quantitative Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators
A very general positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another general positive sublinear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Additionally, two examples of very general specialized operators are presented fulfilling all the above properties, the higher order of approximation of these operators is also considered. It follows .
- 1.G.A. Anastassiou, High order approximation by univariate shift-invariant integral operators, in Nonlinear Analysis and Applications, 2 Volumes, vol. I, ed. by R. Agarwal, D. O’Regan (Kluwer, Dordrecht, 2003), pp. 141–164Google Scholar
- 3.G.A. Anastassiou, Approximation by shift invariant univariate sublinear-Shilkret operators (2018). SubmittedGoogle Scholar