Abstract
We present the basic fuzzy Korovkin theorem via a fuzzy Shisha–Mond inequality given here. This determines the degree of convergence with rates of a sequence of fuzzy positive linear operators to the fuzzy unit operator. The surprising fact is that only the real case Korovkin assumptions are enough for the validity of the fuzzy Korovkin theorem, along with a natural realization condition fulfilled by the sequence of fuzzy positive linear operators. The last condition is fulfilled by almost all operators defined via fuzzy summation or fuzzy integration. This chapter relies on [18].
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© 2010 Springer-Verlag Berlin Heidelberg
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Anastassiou, G.A. (2010). BASIC FUZZY KOROVKIN THEORY. In: Fuzzy Mathematics: Approximation Theory. Studies in Fuzziness and Soft Computing, vol 251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11220-1_7
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DOI: https://doi.org/10.1007/978-3-642-11220-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11219-5
Online ISBN: 978-3-642-11220-1
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