Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators

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DOI:

https://doi.org/10.4067/S0719-06462018000100001

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.

Keywords

Jackson type inequality , Shilkret integral , modulus of continuity , shift invariant , global smoothness preservation , quantitative approximation
  • Pages: 01-16
  • Date Published: 2018-10-19
  • Vol. 20 No. 1 (2018)

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.

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Published

2018-10-19

How to Cite

[1]
G. A. Anastassiou, “Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators”, CUBO, vol. 20, no. 1, pp. 01–16, Oct. 2018.

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Vol. 20 No. 1 (2018)

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