International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 309505 | https://doi.org/10.1155/S0161171287000322

M. K. Aouf, "On coefficient bounds of a certain class of p-valent λ-spiral functions of order α", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 309505, 8 pages, 1987. https://doi.org/10.1155/S0161171287000322

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

Received11 Apr 1986

Abstract

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.

Copyright © 1987 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.


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