A class of analytic functions related to convexity and functions with bounded turning. (English) Zbl 1484.30033
Summary: In this paper, we define a new subclass \(k-\mathcal{Q} (\alpha)\) of analytic functions, which generalizes the class of \(k\)-uniformly convex functions. Various interesting relationships between \(k-\mathcal{Q} (\alpha)\) and the class \(\mathcal{B}(\delta)\) of functions with bounded turning are derived.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
Keywords:
analytic functions; convex functions; uniformly convex functions; functions with bounded turning; subordinationReferences:
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