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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Markov, S. Calculus for interval functions of a real variable. Computing 22, 325–337 (1979). https://doi.org/10.1007/BF02265313
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02265313