Subclasses of regular and schlicht functions with fixed coefficient |
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Authors: | V. A. Pokhilevich |
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Affiliation: | (1) Kiev Polytechnic Institute, USSR |
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Abstract: | In the open unit disk E={z, ¦z¦<1} we consider the class of regular functions q(z) = 1 + 2(1 = )e1zn + 2pn+kzn+k + ..., Re q(z)>, , [0, 1), [0, 2] and fixed, n, kN; fixing zE, we construct the range of the functional I0=q(z). We find an analog of V. A. Zmorovich's variational formula for the expression zp'(z) and point out some applications.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 813–820, June, 1991. |
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