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Upper bound of second Hankel determinant for a new class of analytic functions. (English) Zbl 1250.30006

Summary: In the present investigation an upper bound for the second Hankel determinant \(|a_2a_4 - a_3^2 |\) for functions belonging to the class \(R^\tau_\gamma (A,B)\) is studied using Toeplitz determinants.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
15B05 Toeplitz, Cauchy, and related matrices
15A15 Determinants, permanents, traces, other special matrix functions
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