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

Miskolc Mathematical Notes

article

Muhammad Arif¹  Mohsan Raza²  Miraj Ul Haq¹  Gautam Srivastava³ 

[1] Department of Mathematics, Abdul Wali Khan University;Department of Mathematics, Government College University, Faisalabad;Department of Mathematics and Computer Science, Brandon University;Research Center for Interneural Computing, China Medical University

关键词: Bernardi integral operator;    Janowski functions;    trigonometric functions;   

DOI  :  10.18514/MMN.2020.3146

学科分类：数学（综合）

来源: Miskolci Egyetem

【 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.

【 授权许可】

CC BY