Inclusion results for certain subclasses of spiral-like multivalent functions involving a generalized fractional differintegral operator

作者：Tang, Huo^*; Deng, Guan-Tie; Li, Shu-Hai; Aouf, M. K.

来源：Integral Transforms and Special Functions, 2013, 24(11): 873-883.

DOI：10.1080/10652469.2013.766186

• multivalent functions
• spiral-like functions
• Hadmard product
• subordination
• fractional differintegral operator
• 30C45

Let A(p) denote the class of analytic and p-valent functions in the open unit disc U = {z:vertical bar z vertical bar < 1}. Put
G(p,eta,mu)(lambda)(z) = z(p) + Sigma(infinity)(n=1)(1 + p)(n)(1 + p + eta - mu)(n)/(1 + p - mu)(n)(1 + p + eta -lambda)(n)z(n+p)
(p is an element of N; mu, eta is an element of R; mu < p + 1; -infinity < lambda < eta + p + 1)
and define [G(p,eta,mu)(lambda)(z)]((-1)) in terms of the Hadmard product (or convolution)
G(p,eta,mu)(lambda)(z) * [G(p,eta,mu)(lambda)(z)]((-1)) = z(p)/(1 - z)(delta+p) (delta > -p; z is an element of U).
In this paper, we introduce certain new subclasses of spiral-like multivalent functions defined by using the operator
H(p,eta,mu)(lambda,delta)f(z) = [G(p,eta,)mu(lambda)(z)]((-1)) * f(z)
and investigate several inclusion properties of these classes. Also, some applications involving integral operator are considered.

• 单位
  北京师范大学; 赤峰学院