International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 259-266
doi:10.1155/S0161171287000322
On coefficient bounds of a certain class of p-valent λ-spiral functions of order α
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.
Abstract
Let Sλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1}, which satisfy for z=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z),
w(z) is analytic in U with w(0)=0 and |w(z)|≦|z| for z∈U. In this paper we obtain the bounds of an and we maximize |ap+2−μap+12| over the class Sλ(A,B,p,α) for complex values of μ.