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A class of analytic functions defined by Ruscheweyh derivative

K. S. Padmanabhan, M. Jayamala (1991)

Annales Polonici Mathematici

The function (p ∈ ℕ = 1,2,3,...) analytic in the unit disk E is said to be in the class if (, where and h is convex univalent in E with h(0) = 1. We study the class and investigate whether the inclusion relation holds for p > 1. Some coefficient estimates for the class are also obtained. The class of functions satisfying the condition is also studied.

A maximum principle for the Bergman space.

Boris Korenblum (1991)

Publicacions Matemàtiques

Let f(z) and g(z) be holomorphic in the open unit disk D and let Zf and Zg be their zero sets. If Zf ⊃ Zg and |f(z)| ≥ |g(z)| (1/2 e-2 < |z| < 1), then || f || ≥ || g || where || · || is the Bergman norm: || f ||2 = π-1 ∫D |f(z)|2 dm (dm is the Lebesgue area measure).

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