On the Strong Starlikeness of the Bernardi Transform

Abstract

Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions g, such that |arg{g′(z)}| απ2 in the open unit disk Δ where 0α2. Our results include the results of Mocanu, Nunokawa and others on the Libera transform.

Keywords

• Nunokawa’s lemma
• Libera operator
• Bernardi operator
• strongly starlike functions