Abstract: | We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. |