On coefficient bounds of a certain class ofp-valentλ-spiral functions of orderα

Abstract

LetSλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functionsf(z)=zp+∑n=p+1∞anznanalytic inU={z:|z|<1}, which satisfy forz=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z),w(z)is analytic inUwithw(0)=0and|w(z)|≦|z|forz∈U. In this paper we obtain the bounds ofanand we maximize|ap+2−μap+12|over the classSλ(A,B,p,α)for complex values ofμ.