We propose to determine the values of R such that f(z) is univalent
and starlike for |z| < R under the assumption (i) Re(g(z)∕z) > 0, or (ii)
Re(zg′(z)∕g(z)) > α,0 ≦ α < 1.
We also consider the case when n = 1 and Re(g(z)∕z) > 1∕2
and show that under condition (a) f(z) is univalent and starlike for
|z| < (1 − λ)∕(3 + λ).
![Re(f(z)∕[λf(z)+ (1− λ)g(z)]) > 0](a222x.png)
![|f(z)∕[λf(z)+ (1− λ)g(z)]− 1| < 1 for |z| < 1,0 ≦ λ < 1.](a223x.png)
