Generalizations of p-valent functions via the hadamard product

Abstract

The classes of univalent prestarlike functions Rα, α≥−1, of Ruscheweyh [1] and a certain generalization of Rα were studied recently by Al-Amiri [2]. The author studies, among other things, the classes of p-valent functions R(α+p−1) where p is a positive integer and α is any integer with α+p>0. The author shows in particular that R(α+p)⊂R(α+p−1) and also obtains the radius of R(α+p) for the class R(α+p−1).

Keywords

• p-valent starlike functions
• p-valent close-to-convex functions
• Hadamard product.