ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Vol. LXXVIII, 1(2009)
p. 121 - 135

Some families of p-valent functions with negative coefficients

M. K. Aouf

Received: January 28, 2008;   Accepted: April 8, 2008



Abstract.   We introduce two subclasses   T*(p, α, j)   and  C(p, α, j)   (0 £ α < p j + 1,   1 £ j £ p,
p Î N = {1, 2,...}) of p-valent starlike and p-valent convex functions with negative coefficents. In this paper we obtain coefficient inequalities, distortion theorems, extreme points and integral operators for functions belonging to the classes   T*(p, α, j)   and  C(p, α, j).   We also determine the radii of close-to-convexity and convexity for the functions belonging to the class   T*(p, α, j).   Also we obtain several results for the modified Hadamard products of functions belonging to the classes   T*(p, α, j)   and  C(p, α, j).

Keywordsp-valent; extreme points; modified Hadamard product  

AMS Subject classification: Primary:  30C45;


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Acta Mathematica Universitatis Comenianae
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