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

Abstract

Abstract. In this paper, we further investigate the class of functions φ * (n, p, λ, α) which are analytic in the open unit disk △ = {z : |z| < 1}, 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 φ * (n, p, λ, α), which extend the corresponding results obtained by Altintaş et al.

Extreme Points and Support Points of a Class of Analytic Functions with Fixed Finitely Many Coefficients

“…This relation shall be denoted by f ≺ F . Indeed, some authors have given the extreme points and support points of several subclass of T n , see [2,5,6,8,10]. Here, we want to introduce and study another subclasses…”