×

Neighborhoods of classes of analytic functions. (English) Zbl 0935.30009

Summary: For \(f(z)= z- \sum_{n=2}^\infty a_nz^n\), \(a_n\geq 0\), analytic in the unit disk and either starlike or convex of a positive order, we define a neighborhood of \(f\) and determine how large the neighborhood can be and still contain only functions within specified families. All results are sharp.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDFBibTeX XMLCite