On a subclass ofα-convexλ-spiral functions

F. M. Al-Oboudi, M. M. Hidan
2002 International Journal of Mathematics and Mathematical Sciences  
LetHdenote the class of functionsf(z)=z+∑k=2∞akzkwhich are analytic in the unit discΔ={z:|z|<1}. In this paper, we introduce the classMαλ[A,B]of functionsf∈Hwithf(z)f′(z)/z≠0, satisfying forz∈Δ:{(eiλ−αcosλ)(zf′(z)/f(z))+αcosλ(1+zf″(z)/f′(z))}≺cosλ((1+Az)/(1+Bz))+isinλ, where≺denotes subordination,αandλare real numbers,|λ|<π/2and−1≤B<A≤1. Functions inMαλ[A,B]are shown to beλ-spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.
doi:10.1155/s0161171202011110 fatcat:tfrondvosbgkrjluoa4hvdb4oy