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We solve the problem of finding the range Ω of one functional on the class of pairs of normalized univalent functions. Using the method of internal variations, we obtain a system of functionaldifferential equations for the boundary functions solved in quadratures. We prove that the range of the functional is some disk centered at the origin of a radius depending on the parameters of the functional.
The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.
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