International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 259-266

On coefficient bounds of a certain class of p-valent λ-spiral functions of order α

M. K. Aouf1,2

1Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura, Egypt
2Department of Mathematics, Faculty of Science, University of Qatar, P.O. Box 2713, Doha, Qatar

Received 11 April 1986

Copyright © 1987 M. K. Aouf. 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 Sλ(A,B,p,α)(|λ|<π2, 1A<B1 and 0α<p), denote the class of functions f(z)=zp+n=p+1anzn analytic in U={z:|z|<1}, which satisfy for z=reiθUeiλsecλzf(z)f(z)ip tanλ=p+[pB+(AB)(pα)]w(z)1+Bw(z), w(z) is analytic in U with w(0)=0 and |w(z)||z| for zU. In this paper we obtain the bounds of an and we maximize |ap+2μap+12| over the class Sλ(A,B,p,α) for complex values of μ.