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Results & Lemmas (2)
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LEMMA 1.
LEMMA 1. Let bo>0 and bk a non-increasing sequence of non-negative real numbers satisfying (2k)b2k^(2k-l)b2k^ (keN). (4) Then, for neN, 2…
LEMMA 1. Let bo>0 and bk a non-increasing sequence of non-negative real numbers satisfying (2k)b2k^(2k-l)b2k^ (keN). (4) Then, for neN, 2 bk cos(k<p) > 0 (0 < cp < JI), (5) k=0 and n 2 bk sin(kcp) > 0 (0 < cp < n). (6)
LEMMA 2.
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LEMMA 2. Let f be analytic in D, /(0) = 0, /'(0) = 1, and assume, that f is typically real in D and satisfies Re/'(z) > 0, z eD. Then f is…
LEMMA 2. Let f be analytic in D, /(0) = 0, /'(0) = 1, and assume, that f is typically real in D and satisfies Re/'(z) > 0, z eD. Then f is starlike univalent in D. Glasgow Math. J. 29 (1987) 141-142.
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