Bounds on the curvature for functions with bounded boundary rotation of order 1 − b

M. A. Nasr

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-6

Abstract:

Let V k ( 1 − b ) , k ≥ 2 and b ≠ 0 real, denotes the class of locally univalent analytic functions f ( z ) = z + ∑ n = 2 ∞ a n z n in D = { z : | z | < 1 } such that ∫ 0 2 π | Re { 1 + 1 b z f ″ ( z ) f ′ ( z ) } | d θ < π k , z = r e i θ ∈ D . In this note sharp bounds on the curvature of the image of | z | = r , 0 < r < 1 , under a mapping f belonging to the class V k ( 1 − b ) have been obtained.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:450787

DOI: 10.1155/S016117128600008X

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