On Some Types of Functions in Nonstandard Analysis
Keywords:
Nonstandard Analysis, Limited Function, Continuity, s-Continuity, g-ContinuityAbstract
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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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.
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
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Section
Science Journal of University of Zakho
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Copyright (c) 2016 Ibrahim O. Hamad, Sebar H. Jumha
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How to Cite
On Some Types of Functions in Nonstandard Analysis. (2016). Science Journal of University of Zakho, 4(2), 253-257. https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/358
