Open AccessOn meromorphic $ \alpha $-close-to-convex function
Author(s) -
B. Bharati,
Rajalakshmi Rajagopal
Publication year - 2001
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.32.2001.360
Subject(s) - meromorphic function , combinatorics , mathematics , alpha (finance) , regular polygon , function (biology) , pure mathematics , geometry , statistics , construct validity , evolutionary biology , biology , psychometrics
Let $ B(alpha) $ denote the class of all functions $ f $ meromorphic in the unit disc $ E $ with $ z f(z) e 0 $, $ z^2 f'(z) e 0 $ in $ E $ satisfying the condition
$$ int_{heta_1}^{heta_2} Re left{ alpha (1+z frac{f''(z) }{f'(z)} +(1- alpha) z frac{f'(z) }{f(z)} ight} d heta < pi $$
where $ 0 le heta_1 < heta_2 le heta_2 + 2 pi $, $ z = re^{i heta} $, $ r < 1 $ and $ alpha $ is a non-negative real numbers. We call $ f in B (alpha) $ a meromorphic $ alpha $-colse-to-convex function. This paper pertains to the study of some interesting properties of the class $ B (alpha) $.