SUBKELAS FUNGSI CEMBUNG DAN FUNGSI BAK-BINTANG
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Date
1993-09
Authors
RAJA MAAMOR SHAH, RAJA LAILATUL ZURAIDA
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Abstract
Denote by S the class of functions f analytic and univalent in the
open unit disk U = { z : lzl < 1 } and normalised such that f(O) = 0 =
f' (0) - 1.
For k in [0, 1], let B(k) denote the class of functions f in S
which satisfy I A2 (~) - A (~) I ~ k under Marty transformations
2 3
F(z) = [ f((z+~)/(1+~z)) - f(~) ] / (1-l~l 2 )f' (~) , 1~1 < 1. Fork= 0,
we find the general form and sharp coefficient estimates for functions
in the class B(O). We determine that B(O) consists of convex functions.
We also consider the class R(a) consisting of analytic and
normalised functions f in U which satisfy the condition
Re { f' (z) + azf"(z) } > 0, z e U and a ~ 0. We find the value of a
such that R(a) is a subclass of starlike functions in U.
Further,.- we generalize the condition of R(a). Denote by R(a,/3) the
subclass of analytic and normalised functions F in U which satisfy
Re { F' (z) + azF"(z) } > /3, z e U, f3 < 1 and a = -
1 -
1+-c > 0. We obtain
the values of f3 and c so that R(a) consists of starlike functions in U.
For this class, we obtain sharp coefficient estimates and the lower and
upper bounds of IF(z) 1.
X
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LaStly, let T l 1 ~c , f3 J be the class of analytic and
normalised functions F in U which satisfy
Re { ei0 ( F' (z) + azF" (z) - {3 ) } > 0, for some real number 0 , z e U
and f3 < 1. We obtain sharp coefficient estimates for functions in .
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SUBKELAS FUNGSI CEMBUNG DAN FUNGSI BAK-BINTANG