Abstract
Some properties of the algebraical system <I(R),+,o,−>, where <I(R),+,o> is the well known quasinear interval space and “−” is a nonstandard operation such thata−a=o, are given in this paper. The an elementary calculus for interval functions using this nonstandard arithmetic is discussed.
Zusammenfassung
In dieser Arbeit betrachten wir die Menge <I(R),+,o,−> aller Intenvale hinsichtlich der zwei bekannten Verknüpfungen +und o und einer Nicht-Standard-Verknüpfung “−” mit der Eigenschafta−a=o. Eine elementare Differential- und Integralrechnung für intervallwertige Funktionen kann man auf dieser Basis entwickeln.
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Aumann, R. J.: Integral of set-valued funtions. J. math. Analysis Appl.12, 1–12 (1965).
Banks, H. T., Jacobs, M. Q.: A differential calculus for multifunctions. J. math. analisis Appl.29, 246–272 (1970).
Markov, S. M.: Extended interval arithmetic. Compt. rend. Acad. bulg. Sci.30, 1239–1242 (1977).
Hermes, H.: Calculus of set valued functions and control. J. Math. Mech.18, 47–59 (1968).
Moore, R. E.: Interval analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966.
Ratschek, H., Schröder, G.: Über die Ableitung von intervallwertigen Funktionen. Computing7, 172–187 (1971).
Schröder, G.: Differentiation of interval functions. Proc. Amer. Math. Soc.36, 485–490 (1972).
Sunaga, T.: Theory of an interval algebra and its applications to numerical analysis. RAAG Memoirs2, 29–46 (1958).
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Markov, S. Calculus for interval functions of a real variable. Computing 22, 325–337 (1979). https://doi.org/10.1007/BF02265313
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DOI: https://doi.org/10.1007/BF02265313