Majorization Properties for Certain Classes of Analytic Functions Involving a Generalized Differential Operator
Received:March 01, 2012  Revised:May 22, 2012
Key Word: analytic functions   starlike functions   $\beta$-spiral functions   subordination   majorization property   differential operator.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11271045), the Funds of Doctoral Programme of China (Grant No.20100003110004) and the Natural Science Foundation of Inner Mongolia Province (Grant No.2010MS0117).
Author NameAffiliation
Huo TANG School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China
School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China 
Guantie DENG School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China 
Shuhai LI School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China 
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Abstract:
      In this paper, we introduce new subclasses $S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ and $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$ of certain p-valent analytic functions defined by a generalized differential operator. Majorization properties for functions belonging to the classes $S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ and $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$ are investigated. Also, we point out some new or known consequences of our main results.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.05.007
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