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关于某类解析函数的星象性和Ruscheweyh的一个问题(英文) 被引量：4

On the Starlikeness for Certain Subclass of Analytic Functions and a Problem of Ruscheweyh
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摘要 本文引入了一个涉及Ruscheweyh导数的解析函数子类,应用微分从属方法和Carlson-Shaffer算子讨论了它的从属关系和偏差定理;其次,应用单叶函数的性质和一个微分不等式研究了它的星象性条件和覆盖定理.最后,部分地解决了Ruscheweyh的一个问题. In this paper, a subclass of analytic functions involving Ruscheweyh derivatives is introduced. We discusse its subordinate relations and distortion theorems by using differential subordinate method and Carlson-Shaffer operator. Next, we study its condition of starlikeness and covering theorems by using the properties of univalent functions and a differential inequality. Finally, we give a part of answer to a problem of Ruscheweyh.
作者 刘名生
机构地区 华南师范大学数学系
出处 《数学进展》 CSCD 北大核心 2005年第4期416-424,共9页 Advances in Mathematics（China）
基金 This research is supported by the National Natural Science Foundation of China(No. 10471048). E-mail: liumsh@scnu.edu.cn
关键词 从属 星象函数 偏差定理 覆盖定理 subordination starlike function distortion theorem covering theorem
分类号 O174.51 [理学—基础数学]
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参考文献10

  • 1Carlson B C and Shaffer D B. Starlike and prestarlike hypergeometric functions [J]. SIAM J. Math. Anal.,1984, 15: 737-745.
  • 2Ruscheweyh S. New criteria for univalent functions [J]. Proc. Amer. Math. Sci., 1975, 49: 109-115.
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  • 10Liu Mingsheng. On the univalency of certain analytic functions [J]. 数学进展, 1999, 28(4): 368-370.

同被引文献18

  • 1Milhr S S, Mocanu P T. Differential subordination and univalent functions[J]. Michigan Math.J, 1981(28):157- 171.
  • 2Miller S S, Mocanu P T., Univalent, sohutions of Briot - Bouquet differential subordimations [ J ]. J. Differential Equations, 1985 (58) : 297 - 309.
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  • 5Liu M S. On the Univalency for Certain Subclass of Analytic Functions Involving Ruscheweyh Derivatives[J]. Internat.J. Math.Math. Sci. ,2002,31(9) :567 - 576.
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  • 7Singh R, Singh S. Integrals of certain univalent functions[ J]. Proe. Amer. Math. Soc., 1979(77) : 336 - 340.
  • 8Ruscheweyh. SConvolution in Geometric Function Theory[ M]. Montreal: Lea Presses de l'Universite de Montreal, 1982.
  • 9SRIV AST A V A H M, A TIIY A A A. An intergral operator associated with the Hurwitz-lerch zeta function and differential subordination [J] . Intergral Transforms Spec Funct, 2007,18:207 -216.
  • 10CHO N E, KIM I C, SRIVASTAVA H M. Sandwich-type theorems for multivalent functions associated with the Srivatava-Attiya Operator [J]. Applied Mathematics and Computation, 2010, 217: 918 -928.

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数学进展
2005年 第4期

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