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Hadamard Product of Certain Classes of Functions
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K. Piejko
Published/Copyright:
June 9, 2010
Abstract
In this paper we consider the Hadamard product ∗ of regular functions using the concept of subordination. Let P(A, B) denote the class of regular functions subordinated to the linear fractional transformation (1 + Az)/(1 – Bz), where A + B ≠ 0 and |B| ≤ 1. By P(A, B) ∗ P(C, D) we denote the set {ƒ ∗ g : ƒ ∈ P(A, B), g ∈ P(C, D)}. It is known ([London, Math. Japon. 43: 23–29, 1996], [Stankiewicz, Stankiewicz, Folia Sci. Univ. Tech. Resov. Math. 7: 93-101, 1988]), that for some complex numbers A, B, C, D there exist X and Y such that P(A, B) ∗ P(C, D) ⊂ P(X, Y). The purpose of this note is to find the necessary and sufficient conditions for the equality of the classes P(A, B) ∗ P(C, D) and P(X, Y ).
Received: 2004-06-16
Revised: 2004-11-22
Published Online: 2010-06-09
Published in Print: 2005-June
© Heldermann Verlag
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Articles in the same Issue
- On Nicely Definable Forcing Notions
- Sufficiency and Duality in Multiobjective Programming with Generalized (F, ρ)-Convexity
- A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems for the One-Dimensional p-Laplacian
- Separately Nowhere Constant Functions; n-Cube and α-Prism Densities
- The Notion of V-r-Invexity in Differentiable Multiobjective Programming
- Existence for Some Quasilinear Elliptic Systems with Critical Growth Nonlinearity and L1 Data
- Solutions of Nonlinear Singular Boundary Value Problems
- Orthogonal Bases for Spaces of Complex Spherical Harmonics
- Blow up for the Wave Equation with a Fractional Damping
- Hadamard Product of Certain Classes of Functions
