Abstract
We present the fuzzy Korovkin trigonometric theorem via a fuzzy Shisha–Mond trigonometric inequality presented here too. This determines the degree of approximation with rates of a sequence of fuzzy positive linear operators to the fuzzy unit operator. The astonishing fact is that only the real case trigonometric assumptions are enough for the validity of the fuzzy trigonometric Korovkin theorem, along with a very natural realization condition fulfilled by the sequence of fuzzy positive linear operators. The latter condition is satisfied by almost all operators defined via fuzzy summation or fuzzy integration. This chapter is based on [32].
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© 2010 Springer-Verlag Berlin Heidelberg
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Anastassiou, G.A. (2010). FUZZY TRIGONOMETRIC 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_8
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DOI: https://doi.org/10.1007/978-3-642-11220-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11219-5
Online ISBN: 978-3-642-11220-1
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