2007Journal of Mathematical InequalitiesOpen access

Certain subclasses of multivalent prestarlike functions with negative coefficients

M. Κ. Aouf

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Abstract

The object of the present paper is to investigate coefficient estimates for functions belonging to the subclasses R p [, ] and C p [, ] of p-valent -prestarlike functions of order and type with negative coefficients. We obtain extreme points, distortion theorems, integral operators and radii of starlikeness and convexity for functions belonging to the classes R p [, ] and C p [, ] . We also obtain several results for the modified Hadamard products of functions belonging to the classes R p [, ] and C p [, ] .

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The object of the present paper is to investigate coefficient estimates for functions belonging to the subclasses R p [, ] and C p [, ] of p-valent -prestarlike functions of order and type with negative coefficients. We obtain extreme points, distortion theorems, integral operators and radii of starlikeness and convexity for functions belonging to the classes R p [, ] and C p [, ] . We also obtain several results for the modified Hadamard products of functions belonging to the classes R p [, ] and C p [, ] .

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Available abstract

The object of the present paper is to investigate coefficient estimates for functions belonging to the subclasses R p [, ] and C p [, ] of p-valent -prestarlike functions of order and type with negative coefficients. We obtain extreme points, distortion theorems, integral operators and radii of starlikeness and convexity for functions belonging to the classes R p [, ] and C p [, ] . We also obtain several results for the modified Hadamard products of functions belonging to the classes R p [, ] and C p [, ] .

Key concepts: Mathematics, Extreme point, Distortion (music), Convexity, Hadamard transform, Pure mathematics, Convex function, Order (exchange)

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