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1
Content available remote

Hadamard's multiplication theorem - recent developments

100%
Render H.
Colloquium Mathematicum
|
1997
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tom 74
|
nr 1
79-92
2
Content available remote

Algebras of holomorphic functions with Hadamard multiplication

100%
Render H., Sauer A.
Studia Mathematica
|
1996
|
tom 118
|
nr 1
77-100
EN
A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.
3
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Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

100%
Aouf M. K., Shamandy A., Mostafa A. O., Madian S. M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2010
|
tom 64
|
nr 1
EN
Let \(A\) denote the class of analytic functions with the normalization \(f(0)=f^{\prime }(0)-1=0\) in the open unit disc \(U=\{z:\left\vert z\right\vert <1\}\).  Set \[f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),\] and define \(f_{\lambda ,\mu }^{n}\) in terms of the Hadamard product \[f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). \] In this paper, we introduce several subclasses of analytic functions defined by means of the operator \(I_{\lambda ,\mu }^{n}:A\longrightarrow A\), given by \[ I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). \]Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
4
Content available remote

Characterization of α1 and α2-matrices

100%
Bru R., Cvetković L., Kostić V., Pedroche F.
Open Mathematics
|
2010
|
tom 8
|
nr 1
32-40
EN
This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.
5
Content available remote

Topological algebras with an orthogonal total sequence

100%
Render H.
Colloquium Mathematicum
|
1997
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tom 72
|
nr 2
215-222
EN
The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the "coefficient functionals". Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence $(x_n)_{n∈ℕ}$ satisfying $x^2_n=x_n$ and $x_n x_{n+1} = x_{n+1}$ for all n ∈ ℕ.
6
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Content available

Extended results of the Hadamard product of simple sets of polynomials in hypersphere

100%
Ahmed A. E.-S.
Commentationes Mathematicae
|
2006
|
tom 46
|
nr 2
EN
In this paper we study some extended results of the Hadamard product set for several simple monic sets of polynomials of several complex variables in hyperspherical regions, then we obtain the effectiveness conditions for this Hadamard product in hyperspherical regions.
7
Content available remote

When powers of a matrix coincide with its Hadamard powers

100%
Drnovšek R.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
We characterize matrices whose powers coincide with their Hadamard powers.
8
Content available remote

Invariance properties of homomorphisms on algebras of holomorphic functions with the Hadamard product

100%
Render H., Sauer A.
Studia Mathematica
|
1996
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tom 121
|
nr 1
53-65
EN
Let $H(G_1)$ be the set of all holomorphic functions on the domain $G_1.$ Two domains $G_1$ and $G_2$ are called Hadamard-isomorphic if $H(G_1)$ and $H(G_2)$ are isomorphic algebras with respect to the Hadamard product. Our main result states that two admissible domains are Hadamard-isomorphic if and only if they are equal.
9
Content available remote

Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

88%
Zhao J., Sang C.
Open Mathematics
|
2016
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tom 14
|
nr 1
81-88
EN
Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.
10
Content available remote

New bounds for the minimum eigenvalue ofM-matrices

88%
Wang F., Sun D.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1007-1013
EN
Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
11
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Content available

On differential sandwich theorems of analytic functions defined by certain linear operator

88%
Aouf M. K., Seoudy T. M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2010
|
tom 64
|
nr 2
EN
In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.
12
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Content available

Bi-Bazilevič functions of complex order involving Ruscheweyh type q-difference operator

88%
Murugusundaramoorthy G., Bulut S.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2018
|
tom 17
13
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Content available

Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function

75%
Murugusundaramoorthy G., Uma K.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2010
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tom 64
|
nr 2
EN
Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by \(TS^\mu_b(\alpha, \beta, \gamma)\) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class \(TS^\mu_b(\alpha, \beta, \gamma)\). In particular, we obtain integral means inequalities for the function \(f(z)\) belongs to the class \(TS^\mu_b(\alpha, \beta, \gamma)\) in the unit disc.
14
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Classes of meromorphic multivalent functions with Montel’s normalization

75%
Dziok J.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2012
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tom 66
|
nr 2
EN
In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.
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