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ABSTRACT. In this paper we determine the growth rate of the second Hankel determinant of an areally mean p-valent function. This result both extends and unifies previously known results concerning this problem.

Let S denote the class of analytic and univalent functions in D := {z ∈ C : |z| < 1} of the form f (z) = z + ∞ n=2 a n z n . In this paper, we determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in S and its certain subclasses. We also discuss similar problems for typically real functions.2010 Mathematics Subject Classification. Primary 30C45, 30C55.

For f analytic and close to convex in D = {z : |z| < 1}, we give sharp estimates for the logarithmic coefficients γ n of f defined by log f (z) z = 2 ∞ n=1 γ n z n when n = 1, 2, 3. 2000

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