Research articles
Certain classes of $p$-valent analytic functions with negative coefficients and $(\lambda,p)$-starlike with respect to certain points
Adnan Ghazy Alamoush,
Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
Аннотация:
In this article, we consider classes
$S_{s,\lambda}^*(p,\alpha,\beta)$,
$S_{c,\lambda}^*(p,\alpha,\beta)$, and
$S_{sc,\lambda}^*(p,\alpha,\beta)$ of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively,
$(\lambda,p)$-starlike with respect to symmetric points,
$(\lambda,p)$-starlike with respect to conjugate points, and
$(\lambda,p)$-starlike with respect to symmetric conjugate points. Necessary and sufficient coefficient conditions for functions
$f$ belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.
Ключевые слова и фразы:
p-valent functions, univalent functions, Salagean operator, starlike with respect to symmetric points.
MSC: 30C45 Поступила в редакцию: 10.05.2015
Язык публикации: английский