Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators
- George A. Anastassiou ganastss@memphis.edu
Downloads
DOI:
https://doi.org/10.4067/S0719-06462018000100001Abstract
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
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.
Most read articles by the same author(s)
- George A. Anastassiou, Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator , CUBO, A Mathematical Journal: Vol. 20 No. 3 (2018)
- George A. Anastassiou, Caputo fractional Iyengar type Inequalities , CUBO, A Mathematical Journal: Vol. 21 No. 2 (2019)
- George A. Anastassiou, ð˜²âˆ’ fractional inequalities , CUBO, A Mathematical Journal: Vol. 13 No. 1 (2011): CUBO, A Mathematical Journal
- George A. Anastassiou, Fractional Voronovskaya type asymptotic expansions for quasi-interpolation neural network operators , CUBO, A Mathematical Journal: Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal
- George A. Anastassiou, Higher order multivariate Fuzzy approximation by basic neural network operators , CUBO, A Mathematical Journal: Vol. 16 No. 3 (2014): CUBO, A Mathematical Journal
- George A. Anastassiou, Foundations of generalized Prabhakar-Hilfer fractional calculus with applications , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- George A. Anastassiou, Spline left fractional monotone approximation involving left fractional differential operators , CUBO, A Mathematical Journal: Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal
- George A. Anastassiou, Ostrowski-Sugeno fuzzy inequalities , CUBO, A Mathematical Journal: Vol. 21 No. 3 (2019)
- George A. Anastassiou, Right general fractional monotone approximation , CUBO, A Mathematical Journal: Vol. 17 No. 3 (2015): CUBO, A Mathematical Journal
- George A. Anastassiou, Approximation by discrete singular operators , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal