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Quantitative Approximation by Shift Invariant Multivariate Sublinear-Shilkret Operators

  • George A. Anastassiou
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 190)

Abstract

A very general multivariate positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized Shilkret operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also considered. It follows [3].

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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