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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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