On Some Properties of Functions on Convex Galaxies

On Some Properties of Functions on Convex Galaxies

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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 bostik universal primer pro 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 turbo air m3f24-1 - function , such that and is positive unlimited, for all appreciable.