Abstract
Let fbe locally univalent in the unit disc D. We study the integral means of powers |f′| p and obtain upper bounds for them in terms of a solution of an algebraic equation of degree 4. The coefficients of this algebraic equation depend on the parameter p and on the hyperbolic norms of the pre-Schwarzian f″/f′ and Schwarzian derivative Sf Wepresent some results derived from numerical analysis of the polynomial equation.
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