On applications of differential subordination and superordination

Abstract

In the present investigation we obtain the sufficient conditions for normalized analytic functions $f$ to satisfy

$$ q_1 \prec \frac{f^2}{z^2f'} \prec q_2, $$

where $ q_1 $ and $ q_2 $ are univalent functions with $ q_1(0)= q_2(0)=1 $. Also we obtain the sandwich results involving Carlson-Shaffer linear operator, $ S\u{a}l\u{a} $gean derivative and Ruscheweyh derivative.