Sufficient conditions for \(\varepsilon\) quasi-convex mappings in a complex Banach space. (English) Zbl 1277.32003
Summary: Some sufficient conditions for \(\varepsilon\)-quasi-convex mappings on the unit ball \(B\) in a complex Banach space are provided. From these, we may construct many concrete quasi-convex mappings on \(B\). Some results, presented in this article, generalize related results of earlier authors.
MSC:
32A30 | Other generalizations of function theory of one complex variable |
32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
Keywords:
locally biholomorphic mapping; biholomorphic mapping; starlike mapping; quasi-convex mappingReferences:
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