SUFFICIENT CONDITIONS FOR STARLIKENESS
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참고문헌
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초록
We obtain the conditions on β so that 1+βzp′(z) ≺ 1+4z/3+ 2z2/3 implies p(z) ≺ (2+z)/(2−z), 1+(1−α)z, (1+(1−2α)z)/(1−z), (0 ≤ α < 1), exp(z) or √1 + z. Similar results are obtained by considering the expressions 1+βzp′(z)/p(z), 1+βzp′(z)/p2(z) and p(z)+βzp′(z)/p(z). These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition | log(zf′(z)/f(z))| < 1 or |(zf′(z)/f(z))2 −1| < 1 or zf′(z)/f(z) lying in the region bounded by the cardioid (9x2 + 9y2 − 18x + 5)2 − 16(9x2 + 9y2 − 6x + 1) = 0.
Abstract
We obtain the conditions on β so that 1+βzp′(z) ≺ 1+4z/3+ 2z2/3 implies p(z) ≺ (2+z)/(2−z), 1+(1−α)z, (1+(1−2α)z)/(1−z), (0 ≤ α < 1), exp(z) or √1 + z. Similar results are obtained by considering the expressions 1+βzp′(z)/p(z), 1+βzp′(z)/p2(z) and p(z)+βzp′(z)/p(z). These results are applied to obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy the condition | log(zf′(z)/f(z))| < 1 or |(zf′(z)/f(z))2 −1| < 1 or zf′(z)/f(z) lying in the region bounded by the cardioid (9x2 + 9y2 − 18x + 5)2 − 16(9x2 + 9y2 − 6x + 1) = 0.
참고문헌 (13)
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