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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Burgin, M., Duman, O. Approximations by linear operators in spaces of fuzzy continuous functions. Positivity 15, 57–72 (2011). https://doi.org/10.1007/s11117-009-0041-4
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DOI: https://doi.org/10.1007/s11117-009-0041-4