On coefficient bounds of a certain class of p-valent λ-spiral functions of order α
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...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000322 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |