An improvement of Ozaki's P-valent conditions

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• 作者：Mamoru Nunokawa ; Nak Eun Cho ; Oh Sang Kwon…
• 关键词：Analytic functions ; univalent functions ; Ozaki’s condition
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：32
• 期：4
• 页码：406-410
• 全文大小：152 KB
• 参考文献：[1]Nunokawa, M.: On the theory of multivalent functions. Tsukuba J. Math., 11, 273–286 (1987)MathSciNet MATH
  [2]Nunokawa, M.: On properties of non-Carathéodory functions. Proc. Japan Acad. Ser. A, 68(6), 152–153 (1992)MathSciNet CrossRef MATH
  [3]Nunokawa, M.: On the order of strongly starlikeness of strongly convex functions. Proc. Japan Acad. Ser. A, 69(7), 234–237 (1993)MathSciNet CrossRef MATH
  [4]Ozaki, S.: On the theory of multivalent functions II.Sci. Rep. Tokyo Bunrika Daigaku Sect. A, 3, 45–87 (1941)MathSciNet MATH
  
• 作者单位：Mamoru Nunokawa (1)
  Nak Eun Cho (2)
  Oh Sang Kwon (3)
  Janusz Sokół (4)
  
  1. University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan
  2. Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan, 608-737, Korea
  3. Department of Mathematics, Kyungsung University, Busan, 608-736, Korea
  4. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

The old result due to [Ozaki, S.: On the theory of multivalent functions II. Sci. Rep. Tokyo Bunrika Daigaku Sect. A, 45–87 (1941)], says that if \(f\left( z \right) = {z^p} + \sum\nolimits_{n = p + 1}^\infty {{a_n}} {z^n}\) anzn is analytic in a convex domain D and for some real α we have Re{exp(iα)f(p)(z) >} 0 in D, then f(z) is at most p-valent in D. In this paper, we consider similar problems in the unit disc D = {z ∈ C: |z| < 1}.