The purpose of the present paper is to establish some interesting results on the generalizations of quasi-Hadamard product of functions belonging to the classes of p-valent starlike and p-valent convex functions of order α in the open unit disc U. Our results improve the results of previous authors to the case when r and s are any positive real numbers such that s > 1. It is worth noting that t...

In a recent paper [2], G. R. Blakley raised a question about the decomposition of a ^-valent starlike function into the product of two ^-valent starlike functions. It is the purpose of this note to prove the conjecture of Blakley. Definition 1. The function/(z), regular in |z| <1, is said to be in the class S(p, m), where p and m are positive integers with p^m, if and only if (1) there exists a...