Properties of Certain Nonlinear Integral Operator Associated with Janowski Starlike and Convex Functions

Abstract:

      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.