Properties of Certain Nonlinear Integral Operator Associated with Janowski Starlike and Convex Functions
Received:August 22, 2015  Revised:January 13, 2016
Key Words: analytic functions   Janowski functions   nonlinear integral operators   functions with bounded boundary rotation   subordination  
Fund Project:Supported by the Scientific Research Fund of Sichuan Provincial Education Department (Grant No.14ZB0364).
Author NameAffiliation
Liangpeng XIONG School of Mathematics and Statistics, Wuhan University, Hubei 430072, P. R. China
Department of Mathematics, Engineering and Technical College, Chengdu University of Technology, Sichuan 614007, P. R. China 
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      In this paper, we consider a general nonlinear integral operator $\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n$; $g_1,\ldots,g_n)(z)$. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between $\mathscr{H}_{\alpha_i,\beta_i}(f_1,\ldots,f_n;g_1,\ldots,g_n)(z)$ and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.
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