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

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.