Vol. 56, No. 2, 1975

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Coefficient bounds for some classes of starlike functions

Roger W. Barnard and John Lawson Lewis

Vol. 56 (1975), No. 2, 325–331
Abstract

Let t be given, 14 t , and let S(t) denote the class of normalized starlike univalent functions f in |z| < 1 satisfying (i) |f(z)∕z|t, |z| < 1, if 14 t 1, (ii) |f(z)∕z|t, |z| < 1, if 1 < t . If f(z) = z + Σk=2xakzk S(t) and n is a fixed positive integer, then the authors obtain sharp coefficient bounds for |an| when t is sufficiently large or sufficiently near 14. In particular a sharp bound is found for |a3| when 14 t 1 and 5 t . Also a sharp bound for |04| is found when 14 t 1 or 12.259 t .

Mathematical Subject Classification
Primary: 30A34
Milestones
Received: 4 December 1973
Published: 1 February 1975
Authors
Roger W. Barnard
John Lawson Lewis