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Title: ある解析関数の凸型半径について
Other Titles: On the radius of convexity for some analytic functions
Authors: 吉開, 利秋
Authors (alternative): Yoshikai, Toshiaki
Issue Date: 25-Dec-1971
Citation: 長崎大学教養部紀要. 自然科学. 1971, 12, p.1-5
Abstract: Let S*(α) denote the class of functions analytic in / z / <1 and of the form f(z)=z+a2z2+…………, such shat Re{zf'(z)/f(z)}>α,0≦α<1, for / z / <1. Furthermore let S*(a,α) denote the sub-class of S*(α), consisting of functions F(z)=z+ az2+…………which are starlike of order α with respect to the origin, that is, satisfying the condition Re{zF'(z)/F(z)}>α,0≦α<1, for / z / <1. The functions in S*(a,α) are univaleut in / z / <1. In a recent paper David E. Tepper 〔1〕 gave the sharp lower bounds ro(a) for the radius of convexity which depend on the second coefficient in S*(a,o). In this note we generalize the results of Tepper to the class of functions in S*(a,α).
URI: http://hdl.handle.net/10069/16472
ISSN: 02871319
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:Volume 12

Citable URI : http://hdl.handle.net/10069/16472

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