A Class of Multivalent Functions with Positive Coefficients Defined by Convolution
نویسندگان
چکیده
For a given p-valent analytic function g with positive coefficients in the open unit disk ∆, we study a class of functions f(z) = z + ∑∞ n=m anz , an ≥ 0 satisfying 1 p < ( z(f ∗ g)′(z) (f ∗ g)(z) ) < α ( z ∈ ∆; 1 < α < m+ p 2p ) . Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.
منابع مشابه
Some properties for a class of meromorphically multivalent functions with linear operator
Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we define a subclass $mathcal {T}_{p}(a, c, gamma, lambda; h)$ of meromorphically multivalent functions. The main object of this paper is to investigate some important properties for the class. We also derive many results for the Hadamard roducts of functions belong...
متن کاملSome properties of extended multiplier transformations to the classes of meromorphic multivalent functions
In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.
متن کاملApplications of convolution and subordination to certain $p$-valent functions
In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.
متن کاملA Certain Subclass of Meromorphically Multivalent Analytic Functions with Negative Coefficients
Corresponding Author: Rabha W. Ibrahim Faculty of Computer Science and IT, University Malaya, 50603 Kuala Lumpur, Malaysia Email: [email protected] Abstract: The paper aims to introduce a certain subclass S * g(A,B,α,p,j) of the class Σ * (p) of meromorphically multivalent functions with negative coefficients, defined by using the definitions of Hadamard product and subordination for two f...
متن کاملApplications of multivalent prestarlike functions
Keywords: Analytic functions Multivalent prestarlike function Linear operator Hadamard product Subordination a b s t r a c t In the paper we introduce general classes of multivalent analytic functions defined by the subordination. In particular, we define the class of multivalent prestarlike functions. By using the Ruscheweyh's duality theory we investigate convolution properties related to mul...
متن کامل