Abstract
Let f be an analytic function in the unit disc |z|<1 on the complex plane mathbb {C}. This paper is devoted to obtaining the correspondence between f(z) and zf'(z) at the point w, 0<|w|=R< 1, such that |f(w)|=min {|f(z)|: f(z)inpartial f(|z|leq R) }. We present several applications of the main result. A part of them improve the previous results of this type.
Highlights
Let H denote the class of analytic functions in the unit disc |z| < on the complex plane C
We establish a relation between w(z) and zw (z) at the point z such that |w(z )| = min{|w(z)| : |z| = |z |} or at the point z satisfying ( . )
For some other geometrical properties of analytic functions, we refer to the papers [ – ]
Summary
Let H denote the class of analytic functions in the unit disc |z| < on the complex plane C. If there exists a point z = R exp(iφ ), ≤ φ < π , < R < , such that min (z) : (z) ∈ ∂ |z| ≤ R = (z ) ,
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