A Note on Multivalent Starlike Functions

A Note on Multivalent Starlike Functions

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...

On Some Classes of Multivalent Starlike Functions

Classes of multivalent functions analogous to certain classes of univalent starlike functions are defined and studied. Estimates on coefficients and distortion are made, using a variety of techniques. 1. Let St denote the class of all functions/(z) = z + . . . analytic, univalent and starlike in the unit disc U. Such functions satisfy the condition Re(z/'(z)//(z)) >0,zGU. The problem of definin...

A New Criterion for Multivalent Starlike Functions

The main purpose of the present paper is to derive a new criterion for mul-tivalent starlike functions by applying Jack's lemma.

Some Criteria for Strongly Starlike Multivalent Functions

By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.

On Certain Multivalent Starlike or Convex Functions with Negative Coefficients