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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.

The logarithmic coefficients γ n of an analytic and univalent function f in the unit diskIn the present paper, we consider closeto-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of |γ n |, n = 1, 2, 3 for such functions f .

Let F 1 (F 2 respectively) denote the class of analytic functions f in the unit disk |z| < 1 withFor any fixed z 0 in the unit disk and λ ∈ [0, 1), we shall determine the region of variability for log f (z 0 ) when f ranges over the class {f ∈ F 1 : f (0) = −λ} and {f ∈ F 2 : f (0) = 3λ}, respectively.

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