Radius problems in the class S L*

Janusz Sokół

doi:10.1016/j.amc.2009.04.031

2009-08-01

PRE

Janusz Sokół *

DOI：10.1016/j.amc.2009.04.031

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摘要

En 中文

Let S L* denote the class of all analytic functions f in the unit disc u with the normalization f(0) = f'(0) - 1 = 0 and satisfying the condition vertical bar[zf'(z)/f(z)](2) -1 vertical bar < 1; z is an element of u, thuszf'(z)/f(z) is in the interior of the right half of the lemniscate of Bernoulli (x(2) + y(2))(2)-(x(2) - y(2)) = 0. The relations between S L* and others classes geometrically defined are considered. The radii of alpha-convexity, of alpha-starlikeness (and some of others) of integral is an element of S L* are determined. (c) 2009 Elsevier Inc. All rights reserved.

Keyword:

Analytic functions

Convex functions

Starlike functions

k-Starlike functions

alpha-Starlike functions

alpha-Convex functions

Strongly starlike functions

S L*-functions

Radius of starlikeness

Radius of convexity