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Partial Sums of Starlike and Convex Functions

✍ Scribed by H Silverman

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
135 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let f z szqÝ a z be the sequence of partial sums of a function

a z that is analytic in z -1 and either starlike of order ␣ or ks 2 k Γ„ 4 convex of order ␣, 0 F ␣ -1. When the coefficients a are ''small,'' we deterk Γ„ Ε½ . Ε½ 4 Γ„ Ε½ . Ε½ .4 Γ„ Ε½ . X Ε½ .4 mine lower bounds on Re f z rf z , Re f z rf z , Re fЈ z rf z , and n n n Γ„ X Ε½ . Ε½ .4 Re f z rfЈ z . In all cases, the results are sharp for each n.

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