On Some Types of Functions in Nonstandard Analysis

Authors

  • Ibrahim O. Hamad University of Salahaddin
  • Sebar H. Jumha University of Salahaddin

Keywords:

Nonstandard Analysis, Limited Function, Continuity, s-Continuity, g-Continuity

Abstract

In this paper, by using some nonstandard concepts given by Robinson and axiomatized by Nelson we study the behavior of functions defined on a discrete intervals, whose points are of infinitesimal distances. This study leads to introduce and define some new types of functions in nonstandard analysis and we get some nonstandard results for different nonstandard values (infinitesimals, infinitely close, unlimited …).

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Author Biographies

Ibrahim O. Hamad, University of Salahaddin

Dept. Mathematics, College of Science, University of Salahaddin-Erbil, Hawler, Kurdistan Region-Iraq.

Sebar H. Jumha, University of Salahaddin

Dept. Mathematics, College of Science, University of Salahaddin-Erbil, Hawler, Kurdistan Region-Iraq.

References

Davis, M. (1977). Applied Nonstandard Analysis. New York, John Wiley & Sons.
David R. (2008). Nonstandard Analysis. Springer-Verlag
Diener, F. and Diener, M. (1996). Nonstandard Analysis in Practice, Springer-Verlag, Berlin Heidelberge.
Goldblatt, R. (1998). Lectures on the hyperreals: An introduction to nonstandard analysis, Springer-Verlag, New York, Inc.
Hamad, I. O. (2008). Continuity as a Galaxy of Hyperreal Functions. Raf. J. of Comp . & Math’s., 5(2), pp 85-93.
Nelson, E. (1977). Internal set Theory, Bulletin of the American Mathematical Society, 83(6), 1165-1198.
Robinson, A. (1970). Nonstandard Analysis (2^nd ed.), North-Holland, pub. Comp. Amsterdam.

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Published

2016-12-30

How to Cite

Hamad, I. O., & Jumha, S. H. (2016). On Some Types of Functions in Nonstandard Analysis. Science Journal of University of Zakho, 4(2), 253–257. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/358

Issue

Vol. 4 No. 2 (2016): December, 2016

Section

Science Journal of University of Zakho

License

Copyright (c) 2016 Ibrahim O. Hamad, Sebar H. Jumha

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