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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 3, Pages 425-429

A note on neighborhoods of analytic functions having positive real part

Department of Mathematics, Xavier University, Cincinnati 45207, Ohio, USA

Received 7 July 1989; Revised 18 October 1989

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let P denote the set of all functions analytic in the unit disk D={z||z|<1} having the form p(z)=1+k=1pkzk with Re{p(z)}>0. For δ0, let Nδ(p) be those functions q(z)=1+k=1qkzk analytic in D with k=1|pkqk|δ. We denote by P the class of functions analytic in D having the form p(z)=1+k=1pkzk with Re{[zp(z)]}>0. We show that P is a subclass of P and detemine δ so that Nδ(p)P for pP.