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On Sakaguchi functions. (English) Zbl 1032.30009
Summary: Let \(S_s(\alpha)\) \((0\leq \alpha < 1/2)\) be the class of functions \(f(z)=z+\cdots\) which are analytic in the unit disk and satisfy there \(\text{Re}\{zf'(z)/(f(z)-f(-z))\}>\alpha\). In the present paper, we find the sharp lower bound on \(\text{Re}\{(f(z)-f(-z))/z\}\) and investigate two subclasses \(S_0(\alpha)\) and \(T_0(\alpha)\) of \(S_s(\alpha)\). We derive sharp distortion inequalities and some properties of the partial sums for functions in the classes \(S_0(\alpha)\) and \(T_0(\alpha)\).

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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