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A New Roper‐Suffridge Extension Operator on a Reinhardt Domain
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We introduce a new Roper‐Suffridge extension operator on the following Reinhardt domain
given by where f is a normalized locally biholomorphic function on the unit disc D, pj are positive integer, aj are complex constants, and j = 2, …, n. Some conditions for aj are found under which the operator preserves almost starlike mappings of order α and starlike mappings of order α, respectively. In particular, our results reduce to many well‐known results when all αj = 0.
Title: A New Roper‐Suffridge Extension Operator on a Reinhardt Domain
Description:
We introduce a new Roper‐Suffridge extension operator on the following Reinhardt domain
given by where f is a normalized locally biholomorphic function on the unit disc D, pj are positive integer, aj are complex constants, and j = 2, …, n.
Some conditions for aj are found under which the operator preserves almost starlike mappings of order α and starlike mappings of order α, respectively.
In particular, our results reduce to many well‐known results when all αj = 0.
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