The classes K^ of functions /(z) regular in the unit disc 11 with /(0)= 0,/'(0)= 1 satisfying rleY(z"f)in+l)/(zn-1f)(")]>(n ♦ l)/2 in M are considered and K. , c K , n-0, 1, • • • , is proved. Since Kn is 72 +1 n ' r U the class of functions starlike of order Y2 all functions in K are univalent. Some coefficient estimates are given and special elements of K are determined.

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Abstract.For an analytic function f(z) = z + 2Zk0-2akzk m ^ unit disc E conditions are established such that all functions g(z) = z + 2£-2bkzk e ^«(Z)» i.e. X'k^2^\ak ~ * are m some class of univalent functions in E. For instance, we prove that every g e Nl/4(f) is starlike univalent in E if / is convex univalent.Let A denote the class of analytic functions/in the unit disc E = {z\ \z\ < 1} with /(0) = 0, /'(0) = 1. For /(z) = z -f-2k°.2akzk G A and S > 0 we define the neighborhood Ns(f) as follows.

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