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1
Content available remote Multivariate and abstract approximation theory for Banach space valued functions
Anastassiou G. A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
208--222
EN
Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.
2
Content available remote On differential sandwich theorems of analytic functions defined by certain generalized linear operator
Seoudy T. M., Aouf M. K.
Journal of Mathematics and Applications
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2014
|
Vol. 37
97--109
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.
3
Content available On Jordan-Chevalley decomposition
Bajorska B.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
|
2011
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z. 1
7--27
EN
Expressing a linear operator ƒ on a finite-dimensional vector space over any field K as a sum of two commuting operators – semisimple and nilpotent – is called the Jordan-Chevalley decomposition of ƒ. It is known that this decomposition exists for an arbitrary ƒ if only K is perfect. In this paper we give some methods for determining the decomposition.
PL
Zapis operatora liniowego działającego na skończenie wymiarowej przestrzeni wektorowej nad dowolnym ciałem K w postaci sumy dwóch przemiennych operatorów – półprostego i nilpotentnego – nazywamy rozkładem Jordana-Chevalleya tego operatora.Wiadomo, że jeśli K jest ciałem doskonałym, to taki rozkład istnieje dla dowolnego operatora. Celem artykułu jest omówienie metod wyznaczenia postulowanego rozkładu.
4
Content available remote Rate of convergence for certain mixed family of linear positive operators
Maheshwari P., Sharma D.
Journal of Mathematics and Applications
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2010
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Vol. 33
73-78
EN
The present paper deals with the mixed integrated operators Mn(f; x); which are linear and positive having different basis functions in summation and integration respectively. We estimate the rate of convergence for these operators for functions which have derivatives of bounded variation.
5
Content available remote Applications of a first order differential subordination for analytic functions
Dziok J., Ohriska J.
Journal of Mathematics and Applications
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2010
|
Vol. 32
39-46
EN
In the paper, we define classes of analytic functions, in terms of subordination. By using Jack's Lemma and the Briot-Bouquet differential subordination we obtain some inclusion relations for defined classes.
6
Content available remote A Korovkin type approximation theorem and its application
Büyükyazici Í.
Fasciculi Mathematici
|
2010
|
Nr 45
13-23
EN
In this paper, we investigate a Korovkin-type approximation theorem for sequences of positive linear operators on the space of all continuous real valued functions defined on [a,b]. We also obtain some approximation properties for sequences of positive linear operators constructed by means of the Bernstein operator.
7
Content available remote Subordinations and superordinations using the Dziok-Srivastava linear operator
Oros G. I., Oros O.
Journal of Mathematics and Applications
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2009
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Vol. 31
99-106
EN
By using the properties of the Dziok-Srivastava linear operator we obtain differential subordinations and superordinations by using functions from class A. A sandwich-type result is also given. Theorem 1 from the paper gives sufficient conditions such that a function f ∈ A to be starlike, convex and α-convex.
8
Content available remote Voronovskaja-type theorems and approximation theorems for a class of GBS operators
Pop O. T.
Fasciculi Mathematici
|
2009
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Nr 42
91-108
EN
In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through parti- cular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, Bleimann- Butzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.
9
Content available remote On certain properties of neighborhoods of analytic functions of complex order
Latha S., Poornima N.
Journal of Mathematics and Applications
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2008
|
Vol. 30
83-90
EN
Let A(n) denote the class of functions of the form [wzór] which are analytic in the open unit disk U = {z : |z| < 1}. In this note, the subclasses Sn (β, γ, a, c), Rn (β, γ, a, c; μ ), S(sup α) (sub n) (β, γ a, c) and R (sup α) (sub n) (β, γ, a, c; μ ) of A(n)(are defined and some properties of neighborhoods arę studied for functions of complex order in these classes.
10
Content available remote Classes of functions defined by subordination
Dziok J., Stankiewicz J.
Journal of Mathematics and Applications
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2008
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Vol. 30
53-59
EN
In the paper, we define classes of analytic functions, in terms of subordination. We present some inclusion relations for defined classes.
11
Content available remote Certain class of analytic functions associated with the wright generalized hypergeometric function
Aouf M. K., Dziok J.
Journal of Mathematics and Applications
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2008
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Vol. 30
23-32
EN
Using the Wrigh's generalized hypergeometric function, we introduce a new class W(q, s; A, B, γ) of analytic functions with nega-tive coefficients. In this paper we investigate coefficient estimates, distortion theorem and the radii of convexity and starlikeness.
12
Content available remote Approximate controllability of infinite dimensional systems of the n-th order
Respondek J. S.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 2
199-212
EN
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen’s theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.
13
Content available remote Some parametric family of functions
Dziok J.
Journal of Mathematics and Applications
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2007
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Vol. 29
99-107
EN
In the paper, we define classes of analytic functions, in terms of some linear operator. Coefficients estimates, distortion theorems, and the radii of convexity and starlikeness for this class of analytic functions are given here.
14
Content available remote On certain subclasses of meromorphically multivalent functions associated with a certain linear operator
Aouf M. K., Murugusundaramoorthy G.
Journal of Mathematics and Applications
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2007
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Vol. 29
33-52
EN
In this paper we introduce and study two subclasses (Rn,p(α, A, B)) and Sn,p(α, A, B)) of meromorphic p-valent functions of order α (0 ≤ α < p) defined by certain linear operator. We investigate the various important properties and characteristics of these subclasses. Some properties of neighborhoods of functions in these subclasses are investigated. Also we derive many interesting results for the Hadamard products of functions belonging to the class Sn,p(α, A, B).
15
Content available remote Czynne i bierne operatory stratności - funkcje dwuwymiarowe
Siwczyński M., Krzyk P.
Przegląd Elektrotechniczny
|
2004
|
R. 80, nr 6
624-627
PL
Celem opracowania jest wyodrębnienie z liniowego operatora immitancji obwodu typu dwójnika liniowego niestacjonarnego pewnych podoperatorów, które wyznaczają moc czynną doprowadzoną do układu, oraz tak zwaną moc nieczynną.
EN
The aim of this publication is extraction from a linear two-terminal function operator of non-stationary linear two-terminal network two operators, which evaluate active and reactive power feed.
16
Content available remote On linear operators extending [pseudo]metrics
Banach T., Bessaga C.
Bulletin of the Polish Academy of Sciences. Mathematics
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2000
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Vol. 48, no 1
35-49
EN
For every closed subset X of a stratifiable [respectively metrizable] space Y we construct a positive linear extension operator T : R[sup X*X] --> R[sup Y*Y] preserving constant functions, bounded functions, continuous functions, pseudometrics, metrics, [respectively dominating metrics, and admissible metrics]. This operator is continuous with respect to each of the three topologies : point-wise convergence, uniform, and compact-open. An equivariant analog of the above statement is proved as well.
17
Content available remote Approximation of functions of several variables in exponential weighted spaces
Górzeńska M., Leśniewicz M., Prętki Cz.
Fasciculi Mathematici
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1999
|
Nr 29
23-34
EN
In this note we define some operators Ln and U n of the Szasz-Mirakjan type in exponential weighted spaces of functions of several variables. In Sec. 2 we give some basic properties of these operators. The main theorems are given in Sec. 3. The similar results for functions belonging to polynomial weighted spaces are given in [3]. Some properties of these operators for functions of one variable with exponential weighted spaces are given in [4] .
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