Let f(z) = z + ∑n=2 ∞ a n z n be analytic in the unit disk with the second coefficient a 2 satisfying |a 2 | = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a n | ≤ cn + d (c, d ≥ 0) or |an | ≤ c/n (c > 0 and n ≥ 3). Other radius constants are also obtained for these functions, and connections with earlier results are made.
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机译:令f(z)= z + ∑n = 2 ∞ sup> a n z n sup>在单位圆盘中具有第二个系数a 2满足| a 2 |的解析。 = 2b,0≤b≤1。对于第n个系数满足| a n em> |的函数f,将获得Janowski星状尖锐半径。 ≤ cn em> + d em>( c em>, d em>≥0)或| a em> < em> n em> | ≤ c em> / n em>( c em 0和 n em>≥3)。对于这些功能,还可以获得其他半径常数,并且可以得到较早的结果。
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