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Integral Operators and Univalent Functions
並列摘要
In this paper, we define two new integral operators L(superscript k) and L(subscript k) which are iterative in nature. We show that for f (z)= z+a2z^2+．．．+an z^n+．．．with radius of convergence larger than one, L(superscript k) f (z) and L(subscript k) f (z) when restricted on E = {z : |z| ＜ 1} will eventually be univalent for large enough k. We then show that these are the best possible results by demonstrating that there exists a holomorphic function T (z) in normalized form and with radius of convergence equal to one such that L(superscript k)T (z) and L(subscript k)T (z) fail to be univalent when restricted to E for every k ∈ N.
並列關鍵字
無資料延伸閱讀
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