Analytic functions close to mappings convex in one direction
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- by Walter Hengartner and Glenn Schober PDF
- Proc. Amer. Math. Soc. 28 (1971), 519-524 Request permission
Abstract:
By analogy to the class of close-to-convex functions we define a class of analytic functions which are close to a family $\Sigma$ of mappings onto domains convex in one direction. In contrast to the close-to-convex class the close-to-$\Sigma$ functions are not necessarily univalent. However, we determine the radius of convexity for $\Sigma$, and this gives a lower bound for the radius of univalence of close-to-$\Sigma$ functions. We next derive the coefficient estimate $|{A_n}| \leqq n|{A_1}|$ for close-to-$\Sigma$ functions and conclude with an elementary distortion theorem.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 519-524
- MSC: Primary 30.42
- DOI: https://doi.org/10.1090/S0002-9939-1971-0277704-9
- MathSciNet review: 0277704