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Extreme points and support points of a class of analytic functions with missing coefficients

Xiong L., Tian L, Luo S., Liu X.

Demonstratio Mathematica

2013

Vol. 46, nr 3

525--532

Let Mn(a, b, c) denote a class of functions of the form (...) which are analytic in open unit disk (...) and satisfy the condition (...). In this paper, we obtain the extreme points and support points of the class Mn(a, b, c) of functions.

Some general results and extreme points of p-valent functions with negative coefficients

Xiong L.

Demonstratio Mathematica

2011

Vol. 44, nr 2

261-272

In this paper, we further investigate the class of functions (…) which are analytic in the open unit disk (…),and involve the combinations of the representations of p-valently starlike and convex functions. We obtain several generalized results on the modified-Hadamard product of the class (…) which extend the corresponding results obtained by Altintas et al. [Computers Math. Applic. 30(2), 9-16, (1995)]; Darwish, Aouf [Mathematical and Computer Modelling (2007), doi:10.1016/j.mcm.2007.08.016 ]. Futher, by fixing the second coefficient of functions in (…) we introduce the special class (…) and discuss the extreme points.