On Some Properties of Functions on Convex Galaxies

Ismail, Tahir H.; Sulaiman, Barah M.; Saleh, Hind Y.

doi:10.33899/csmj.2013.163483

	On Some Properties of Functions on Convex Galaxies
AL-Rafidain Journal of Computer Sciences and Mathematics
Article 13, Volume 10, Issue 2, 2013, Pages 165-170 PDF (387.68 K)
Document Type: Research Paper
DOI: 10.33899/csmj.2013.163483
Authors
Tahir H. Ismail¹; Barah M. Sulaiman¹; Hind Y. Saleh²
¹College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq
²College of Basic Education University of Duhok
Abstract
In this paper, we define and study extensively a new type of external sets in , we call it "convex galaxies". We show that these convex external sets may be classified in some definite types. More precisely, we obtain the following : (1)Let be a convex galaxy which is symmetric with respect to zero, then (i) is an - galaxy (0) if and only if there exists an internal strictly increasing sequence of strictly positive real numbers with such that and , for all , where, is some limited real number such that . (ii) is a non-linear galaxy if and only if there exists an internal strictly increasing sequence of strictly positive real numbers with such that is unlimited for all . (2)Let be a convex galaxy which is symmetric with respect to zero, then (i) is an - galaxy (0) iff there exists a real internal strictly increasing - function , such that , and for all limited , where is a positive real number. (ii) is a non-linear galaxy if and only if there exists a real internal strictly increasing - function , such that and is positive unlimited, for all appreciable .
Keywords
Convex; galaxy; External Sets

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