, Volume 22, Issue 4, pp 325–337 | Cite as

Calculus for interval functions of a real variable

  • S. Markov


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.


Computational Mathematic Interval Function Algebraical System Real Variable Interval Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Differential- und Integralrechnung für Intervallfunktionen einer reellen Variablen


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aumann, R. J.: Integral of set-valued funtions. J. math. Analysis Appl.12, 1–12 (1965).Google Scholar
  2. [2]
    Banks, H. T., Jacobs, M. Q.: A differential calculus for multifunctions. J. math. analisis Appl.29, 246–272 (1970).Google Scholar
  3. [3]
    Markov, S. M.: Extended interval arithmetic. Compt. rend. Acad. bulg. Sci.30, 1239–1242 (1977).Google Scholar
  4. [4]
    Hermes, H.: Calculus of set valued functions and control. J. Math. Mech.18, 47–59 (1968).Google Scholar
  5. [5]
    Moore, R. E.: Interval analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966.Google Scholar
  6. [6]
    Ratschek, H., Schröder, G.: Über die Ableitung von intervallwertigen Funktionen. Computing7, 172–187 (1971).Google Scholar
  7. [7]
    Schröder, G.: Differentiation of interval functions. Proc. Amer. Math. Soc.36, 485–490 (1972).Google Scholar
  8. [8]
    Sunaga, T.: Theory of an interval algebra and its applications to numerical analysis. RAAG Memoirs2, 29–46 (1958).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • S. Markov
    • 1
  1. 1.Department of MathematicsUniversity of SofiaSofiaBulgaria

Personalised recommendations