A note on Bazilevič functions (Q5905471)

For \(\alpha>0\), let \(B_ 1(\alpha)\) be the class of normalized analytic functions defined in the open unit disk \(D\) satisfying \(\text{Re}\left({f(z)\over z}\right)^{\alpha-1}f'(z)>0\) for \(z\in D\). The authors obtain the sharp lower bound for \(\text{Re}\left({f(z)\over z}\right)^ \alpha\) and the result is generalized to some iterated integral operators.