Relationship of the Bernardi integral operator with certain classes of analytic functions

[摘要] In this article, we find condition on α so that; if 1+αz((zf′(z))/(f(z)))≺((1+Az)/(1+Bz)), then ((zF′(z))/(F(z)))≺1+sin(z), where F(z)=((γ+1)/(z^{β}))∫₀^{z}t^{γ-1}f(t)dt, is the well-known Bernardi integral operator. We also study the case ((zF′(z))/(F(z)))≺cos(z). Some similar implications are also discussed for both the functions.

[学科分类] 数学（综合）

[关键词] Bernardi integral operator;Janowski functions;trigonometric functions