The Fekete-Szegő problem for subclasses of analytic functions defined by a differential operator related to conic domains. (English) Zbl 1189.30049

Summary: By using a linear multiplier fractional differential operator a new subclass of analytic functions generalized \(\beta\)-uniformly convex functions, denoted by \(\beta-SP^{n,\alpha}_{\lambda,\mu}(\gamma)\), is introduced. For this class the Fekete-Szegő problem is completely solved. Various known or new special cases of our results are also pointed out.


30C50 Coefficient problems for univalent and multivalent functions of one complex variable
26A33 Fractional derivatives and integrals
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
41A35 Approximation by operators (in particular, by integral operators)
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