Abstract

By employing the basic hypergeometric series, we introduce here a linear operator for analytic functions. By means of this linear operator, we define and investigate a class of analytic functions. Also, as an application of Jack's lemma, sufficient conditions for univalence, starlikeness and strong starlikeness of certain analytic functions are obtained.

Keywords: Basic hypergeometric function; subordination; starlike; close to convex; univalent function; S\v{a}l\v{a}gean differential operator; Jack's lemma.

MSC: 30C45

Pages:  1--7     

Volume  65 ,  Issue  1 ,  2013