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In this paper, we study analytic and geometric properties of the solution $q(z)$ to the differential equation $q(z)+zq'(z)/q(z)=h(z)$ with the initial condition $q(0)=1$ for a given analytic function $h(z)$ on the unit disk $|z|<1$ in the complex plane with $h(0)=1.$ In particular, we investigate the possible largest constant $c>0$ such that the condition $|\Im[zf''(z)/f'(z)]|<c$ on $|z|<1$ implies starlikeness of an analytic function $f(z)$ on $|z|<1$ with $f(0)=f'(0)-1=0.$
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참고문헌 (11)
참고문헌 신청
Ch. Pommerenke / 1992 / Boundary Behaviour of Conformal Maps / Springer-Verlag
L. Lewin / 1981 / Polylogarithms and Associated Functions / North-Holland Publishing Co
M. Li / 2015 / Some extentions of the Open Door Lemma / Studia Univ. Babes-Bolyai Math 60 : 421 ~ 430
M. Tsuji / 1959 / Potential Theory in Modern Function Theory / Maruzen
P. L. Duren / 1983 / Univalent Functions / Springer-Verlag
L. Lewin / 1981 / Polylogarithms and Associated Functions / North-Holland Publishing Co
M. Li / 2015 / Some extentions of the Open Door Lemma / Studia Univ. Babes-Bolyai Math 60 : 421 ~ 430
M. Tsuji / 1959 / Potential Theory in Modern Function Theory / Maruzen
P. L. Duren / 1983 / Univalent Functions / Springer-Verlag
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