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Fekete-Szegő problem for subclasses of uniformly starlike functions with respect to symmetric points. (English) Zbl 1251.30015
Summary: In the present investigation, sharp upper bounds of $$|\eta a^2_2 -a_3|$$ for functions $$f(z)=z+a_2z^2+a_3z^3+\cdots$$ belonging to certain subclasses of uniformly starlike functions with respect to symmetric points are obtained. Also, certain applications of the main results to certain subclasses defined by convolution are considered. In addition, Fekete-Szegő inequalities for certain classes of analytic functions defined by fractional derivatives are also given.
MSC:
 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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