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Results & Lemmas (2)
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Theorem 1.
Theorem 1. Letfe S(ot, P) and let r0 be the smallest positive root of the equation (2.1) (2/J - 1) (2a0 - 1) r4 - 2(2j8 - 1) (2ajS - 1) r3…
Theorem 1. Letfe S(ot, P) and let r0 be the smallest positive root of the equation (2.1) (2/J - 1) (2a0 - 1) r4 - 2(2j8 - 1) (2ajS - 1) r3 - - 2(p + ap + 2aj82 - 1) r2 - 2r + 1 = 0. Then (i) for 0 f_ r < r 0,/ is starlike in \z\ < r_, where rl is the smallest positive root of the equation (2.2) (20 - 1) (2aj? - 1) r2 + 2(3aj3 - fi - 1) r + 1 = 0 , (ii) for r0 ^ r < 1,/ is starlike in \z\ < r2, where r2 is the smallest positive root of the equation (2.3) (I6a0 - 9 - a) r4 - 2(8aj? + 3 - 3a) r2 +
Theorem 2.
Theorem 2. Letf(z) = z + a2z2 +... be in S(a, /?). Then (3.1) |<ij ^ 4)8(1 - a) 1 - 2)8(1 - a) + jj(l - a) n, (n = 2) /or a// t;a/wes of a,…
Theorem 2. Letf(z) = z + a2z2 + ... be in S(a, /?). Then (3.1) |<ij ^ 4)8(1 - a) {1 - 2)8(1 - a) + jj(l - a) n} , (n = 2) /or a// t;a/wes of a, )8 (0 g a < 1, 0 < )8 ^ 1). The resw/f is sharp.
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