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). Keywords: p-valent; extreme points; modified Hadamard product AMS Subject classification: Primary: 30C45; PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |