Approximations by linear operators in spaces of fuzzy continuous functions

Approximations by linear operators in spaces of fuzzy continuous functions In this work, we further develop the Korovkin-type approximation theory by utilizing a fuzzy logic approach and principles of neoclassical analysis, which is a new branch of fuzzy mathematics and extends possibilities provided by the classical analysis. In the conventional setting, the Korovkin-type approximation theory is developed for continuous functions. Here we extend it to the space of fuzzy continuous functions, which contains a great diversity of functions that are not continuous. Furthermore, we give several applications, demonstrating that our new approximation results are stronger than the classical ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Approximations by linear operators in spaces of fuzzy continuous functions

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2009 by The Author(s)
Subject
Mathematics; Econometrics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-009-0041-4
Publisher site
See Article on Publisher Site

Abstract

In this work, we further develop the Korovkin-type approximation theory by utilizing a fuzzy logic approach and principles of neoclassical analysis, which is a new branch of fuzzy mathematics and extends possibilities provided by the classical analysis. In the conventional setting, the Korovkin-type approximation theory is developed for continuous functions. Here we extend it to the space of fuzzy continuous functions, which contains a great diversity of functions that are not continuous. Furthermore, we give several applications, demonstrating that our new approximation results are stronger than the classical ones.

Journal

PositivitySpringer Journals

Published: Jan 12, 2010

References

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