Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators

  • George A. Anastassiou Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Keywords: Jackson type inequality, Shilkret integral, modulus of continuity, shift invariant, global smoothness preservation, quantitative approximation

Abstract

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.

References

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).

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

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

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

Niel Shilkret,Maxitive measure and integration, Indagationes Mathematicae, 33 (1971), 109-116.

Published
2018-10-19
How to Cite
Anastassiou, G. A. (2018). Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators. CUBO, A Mathematical Journal, 20(1), 01-16. https://doi.org/10.4067/S0719-06462018000100001