Goluzina, E. G. Regions of values of the systems \(\{f(z_1),f(z_2),f'(z_2)\}\) and \(\{f(z_1),f'(z_1),f''(z_1)\}\) on the class of typically real functions. (English. Russian original) Zbl 1081.30015 J. Math. Sci., New York 122, No. 6, 3608-3615 (2004); translation from Zap. Nauchn. Semin. POMI 286, 48-61 (2002). Summary: Let \(T\) be the class of functions \(f(z)= z+ a_2 z^2+\cdots\) that are regular in the unit disk and satisfy the condition \(\operatorname {Im} f(z) \operatorname {Im} z> 0\) for \(\operatorname {Im} z\neq0\), and let \(z_1\) and \(z_2\) be any distinct fixed points in the disk \(|z|<1\). For the systems of functionals mentioned in the title, the regions of values on \(T\) are studied. As a corollary, the regions of values of \(f'(z_2)\) and \(f''(z_1)\) on the subclasses of functions in \(T\) with fixed values \(f(z_1)\), \(f(z_2)\) and \(f'(z_1)\), \(f'(z_1)\), respectively, are found. 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