Computing

, Volume 22, Issue 4, pp 325–337

# Calculus for interval functions of a real variable

• S. Markov
Article

## 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.

## Keywords

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

## 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.

## References

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