By applications of Cauchy-Schwarz inequalities, several sufficient conditions in terms of hypergeometric inequalities were found such that the linear operator preserves and transforms certain well known subclasses of univalent functions to another classes. Relevant connections of our work with the earlier work is pointed out.
Key words: Analytic function, subordination, starlike function, convex function, hypergeometric function, Cauchy-Schwarz inequality.
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