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THE FEKETE-SZEGÖ PROBLEM FOR STRONGLY CLOSE-TO-CONVEX FUNCTIONS WITH HADAMARD PRODUCT
Maslina Darus (Malaysia) and Ng Choon Hong (Malaysia)
Abstract
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For 0
< a
£
1 and b
³
1, let MCC(F,
Y;
a,
b)
be the class of function defined in the open
unit disk U by
where g(z) = z + b2z2 + b3z3
+ … is analytic function and satisfies
for some
and
analytic in U such that g(z)
*
Y(z) ¹
0, ln
³
0, gn
³
0 and ln
> gn
(n ³
2). For f
Î
MCC(F,
Y;
a,
b)
and given by f(z) = z + a2z2
+ a3z3
+ … a sharp upper bound is obtained for
when m
³
1. |
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Keywords and phrases:
univalent and analytic functions, Fekete-Szegö problem, Hadamard product. |
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