Goluzina, E. G. Regions of values for the systems \(\{f(z_0), f^{\prime}(z_0),c_2\}\) and \(\{f(r),f^{\prime}(r),f(z_0)\}\) in the class of typically real functions. (English. Russian original) Zbl 1071.30007 J. Math. Sci., New York 118, No. 1, 4753-4759 (2003); translation from Zap. Nauchn. Semin. POMI 276, 41-51 (2001). Summary: Let \(T\) be the class of functions \(f(z)\) having the following properties: these functions are regular and typically real in the disk \(|z|< 1\) and have the expansions \(f(z)= z+ c_2 z^2+ c_3 z^3+\cdots\). We give algebraic and geometric characterizations of regions of values for the functionals in the class \(T\) mentioned in the title. In the same class of functions, we find regions of values for \(f'(z_0)\) with fixed \(c_2\) and \(f(z_0)\) and for \(f(z_0)\) with fixed \(f(r)\) and \(f'(r)\). MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) × Cite Format Result Cite Review PDF Full Text: DOI EuDML