Research on geometric mappings in complex systems analysis. (English) Zbl 1371.30015
Summary: We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order \(\lambda\), in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order \(\lambda\). By the properties of functions with positive real parts and considering the zero of order \(k\), we obtain the coefficient estimates for almost starlike functions of complex order \(\lambda\) on \(D\). We also discuss the invariance of almost starlike mappings of complex order \(\lambda\) on Reinhardt domains and on the unit ball \(B\) in complex Banach spaces. The conclusions contain and generalize some known results.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 32A17 | Special families of functions of several complex variables |
Keywords:
almost star-like functions; distortion results; coefficient estimates; almost star-like mappingsReferences:
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