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On the radii of starlikeness and convexity of certain classes of regular functions

Published online by Cambridge University Press:  09 April 2009

Pran Nath Chichra
Pran Nath Chichra
Affiliation:
Department of Mathematics Punjabi UniversityPatiala, India
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Let Rn denote the class of functions f(z) = z+anzn+ … (n ≧ 2) which are regular in the open disc|z| < 1 (hereafter called E) and satisfy for all z in E. Rnis a subclass of the class of close-to-star function in E [9, p. 61]. MacGregor showed that the radius of univalence and starlikeness of Rn is , see [4,5]. The radius of convexity of R = R2 is r0 = 0.179 …, where r0 is the smallest positive root of the equation 1−5r−3r2−r3 = 0, see [8].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 2 , March 1972 , pp. 208 - 218
Copyright
Copyright © Australian Mathematical Society 1972

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