Application of duality techniques to starlikeness of weighted integral transforms

作者：Ebadian A^*; Aghalary R; Shams S

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2010, 17(2): 275-285.

• Convolution
• Univalent functions
• Hypergeometric function
• Duality technique
• Starlike functions

Let A be the class of normalized analytic functions in the unit disc and let P(gamma)(alpha, beta) be the class of all functions f is an element of A satisfying the condition
there exists eta is an element of R, R{e(i eta) [(1 - gamma) (f(z)/z(a) + gamma zf'(z)/f(z) (f(z)/z)(a) - beta]}0.
We consider the integral transform
V(lambda,a) (f)(z) = {integral(1)(0) lambda(t) (f(tz)/t)(a) dt}(1/a),
where lambda(t) is a real-valued nonnegative weight function normalized by integral(1)(0)lambda (t)dt = 1. In this paper we find conditions on the parameters alpha, beta, gamma, mu such that V(lambda,a)(f) maps P(gamma)(alpha, beta) into the class of starlike functions of order mu. We also provide a number of applications for various choices of A (t). Our results generalize known results on this topic.

• 出版日期2010-6