A class of analytic functions involving in the Dziok-Srivastava operator

作者：Xu, Neng^*; Yang, Ding-Gong; Sokol, Janusz

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013, 2013(1): 138.

DOI：10.1186/1029-242X-2013-138

• uniformly convex functions
• convex univalent functions
• starlike functions
• alpha-spirallike functions
• convolution
• Dziok-Srivastava operator
• subordination

Let A be a class of functions f(z) of the form
f(z) = z + Sigma(infinity)(n=2) a(n)z(n) (0.1)
which are analytic in the open unit disk U. By means of the Dziok-Srivastava operator, we introduce a new subclass
S'(m) (alpha(1), alpha, mu) (l <= m + 1, l, m is an element of N boolean OR {0}, -pi/2 < alpha < pi/2, mu > - cos alpha)
of A. In particular, S-0(1) (2, 0, 0) coincides with the class of uniformly convex functions introduced by Goodman. The order of starlikeness and the radius of alpha-spirallikeness of order beta (beta < 1) are computed. Inclusion relations and convolution properties for the class S'(m) (alpha(1), alpha, mu) are obtained. A special member of S'(m) (alpha(1), alpha, mu) is also given. The results presented here not only generalize the corresponding known results, but also give rise to several other new results.

• 出版日期2013
• 单位苏州大学; 常熟理工学院; 宿州学院