A Note on Multivalent Starlike Functions
نویسنده
چکیده
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 positive p<l such that
منابع مشابه
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...
متن کاملOn a Subclass of Multivalent β-Uniformly Starlike and Convex Functions defined by a Linear Operator
AbstractIn this paper we introduce the subclass K(μ, γ, η, α, β) of β-uniformly convex and β-uniformly starlike functions which are analytic and multivalent with negative coefficients defined by using fractional calculus operators. Characterization property exhibited by the functions in the class and the results of modified Hadamard product are discussed. Connections with the popular subclasses...
متن کاملA 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.
متن کاملMultivalent Harmonic Functions Defined by Dziok-Srivastava Operator
Necessary and sufficient coefficient bounds and convolution condition for certain multivalent harmonic functions whose convolution with generalized hypergeometric functions is starlike of order γ are investigated. Results on extreme points, convex combination and distortion bounds using the coefficient condition are also obtained. 2010 Mathematics Subject Classification: 30C45, 30C50
متن کامل