Φ-like holomorphic functions in 𝐶ⁿ and Banach spaces

Gurganus, Kenneth R.

doi:10.1090/S0002-9947-1975-0374470-1

$\Phi$-like holomorphic functions in $\textbf {C}^{n}$ and Banach spaces
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by Kenneth R. Gurganus

Trans. Amer. Math. Soc. 205 (1975), 389-406

DOI: https://doi.org/10.1090/S0002-9947-1975-0374470-1

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Abstract:

In a recent paper, L. Brickman introduced the concept of $\Phi$-like holomorphic functions as a complete generalization of starlike and spirallike functions of a single complex variable. In the present paper, the author extends this work to locally biholomorphic mappings of several complex variables and then to locally biholomorphic mappings defined in an arbitrary Banach space. Complete characterizations of univalency and starlikeness of locally biholomorphic maps in general Banach spaces are obtained.

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