Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators

  • George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.


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.


[1] G.A. Anastassiou, High order Approximation by univariate shift-invariant integral operators, in: R. Agarwal, D. O’Regan (eds.), Nonlinear Analysis and Applications, 2 volumes, vol. I, pp. 141-164, Kluwer, Dordrecht, (2003).

[2] G.A. Anastassiou, Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, 2011.

[3] G.A. Anastassiou, S. Gal, Approximation Theory, Birkhauser, Boston, Basel, Berlin, 2000.

[4] G.A. Anastassiou, H.H. Gonska, On some shift invariant integral operators, univariate case, Ann. Polon. Math., LXI, 3, (1995), 225-243.

[5] Niel Shilkret, Maxitive measure and integration, Indagationes Mathematicae, 33 (1971), 109-116.
How to Cite
ANASTASSIOU, George A.. Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators. CUBO, A Mathematical Journal, [S.l.], v. 20, n. 1, p. 01-16, oct. 2018. ISSN 0719-0646. Available at: <>. Date accessed: 19 nov. 2018. doi:

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.