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- Title
A covering theorem for typically real functions.
- Authors
Brannan, D. A.; Kirwan, W. E.
- Abstract
Let T denote the class of functionsf(z) = z+a2z2+…that are analytic in U = {|z| <1}, and satisfy the conditionImf(z). Imz≧ 0 (zεU).Thus T denotes the class of typically real functions introduced by W. Rogosinski [5].One of the most striking results in the theory of functionsg(z) = z + b2z2…that are analytic and univalent in U is the Koebe-Bieberbach covering theorem which states that {|w| <¼} ⊂ g(U). In this note we point out that the same result holds for functions in the class T, a fact which seems to have been overlooked previously. We also determine the largest subdomain of U in which every f(z) in T is univalent, extending previous results in [1] and [2].
- Publication
Glasgow Mathematical Journal, 1969, Vol 10, Issue 2, p153
- ISSN
0017-0895
- Publication type
Article
- DOI
10.1017/S0017089500000719