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- W4246891710 abstract "For $delta geqslant 0$ and $f(z) = z + {a_2}{z^2} + cdots$ analytic in $|z| < 1$ let the $delta$-neighborhood of $f$, ${N_delta }(f)$, consist of those analytic functions $g(z) = z + {b_z}{z^2} + cdots$ with $sum nolimits _{k = 2}^infty {k|{a_k} - {b_k}| leqslant delta }$. We determine sufficient conditions guaranteeing which neighborhoods of certain classes of convex functions belong to certain classes of starlike functions. We extend some recent results of St. Ruscheweyh and R. Fournier and, at the same time, provide much simpler proofs. We also prove precisely how boundaries affect the value of $delta$ for some general classes of functions." @default.
- W4246891710 created "2022-05-12" @default.
- W4246891710 creator A5069158228 @default.
- W4246891710 date "1985-02-01" @default.
- W4246891710 modified "2023-09-26" @default.
- W4246891710 title "Some Sharp Neighborhoods of Univalent Functions" @default.
- W4246891710 doi "https://doi.org/10.2307/1999656" @default.
- W4246891710 hasPublicationYear "1985" @default.
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