A generalization of starlike functions

Mapping properties of basic hypergeometric functions

“…For all the above results and further properties related to the class PS q we refer the interested reader to [14]. See also [25] for some continued fraction expansion related to G q .…”

“…BARICZ AND A. SWAMINATHAN We note that in [14] the following result is obtained using the continued fraction results for a circular domain given in [27]. …”

“…For the interested reader on this result and various other continued fraction expansions, [11,13,14,15,27] and references therein may be useful. In particular, the above continued fraction can be obtained as a limiting case of a continued fraction available in [11, p. 488 …”

“…We exhibit one such application in this section. The following definition is given in [14]: an analytic function f is said to belong to the class PS q of generalized starlike functions if for all q ∈ (0, 1) and z ∈ D we have…”

“…In the next section we present some new results on the quotients of basic hypergeometric functions by following some ideas of Küstner [18] on Gaussian hypergeometric functions, while in section 3 we study the generalized starlikeness (introduced by Ismail et al [14]) and convexity of basic hypergeometric functions by using the results of section 2. These results complement the main results from [1,14,18]. The last section is devoted for concluding remarks.…”