A Korovkin-type theorem for sequences of positive linear operators on function spaces

Positivity ◽  
2021 ◽  
Author(s):  
Abderraouf Dorai
Keyword(s):  
Type Theorem ◽  
Function Spaces ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Korovkin Type Theorem

scholarly journals Korovkin-Type Theorems in WeightedLp-Spaces via Summation Process

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tuncer Acar ◽  
Fadime Dirik
Keyword(s):  
Uniform Convergence ◽  
Approximation Theory ◽  
Type Theorem ◽  
Linear Operators ◽  
Multivariate Functions ◽  
Korovkin Type Theorem ◽  
Approximation Theorems ◽  
Convergence Method ◽  
Summation Process ◽  
Korovkin Type Theorems

Korovkin-type theorem which is one of the fundamental methods in approximation theory to describe uniform convergence of any sequence of positive linear operators is discussed on weightedLpspaces,1≤p<∞for univariate and multivariate functions, respectively. Furthermore, we obtain these types of approximation theorems by means of𝒜-summability which is a stronger convergence method than ordinary convergence.

scholarly journals The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Behar Baxhaku ◽  
Ramadan Zejnullahu ◽  
Artan Berisha
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Space ◽  
Type Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weighted Modulus Of Continuity ◽  
Rate Of Approximation ◽  
Szász Operators ◽  
Weighted Modulus

We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.

scholarly journals A Korovkin type theorem for weighted spaces of continuous functions

1997 ◽  
Vol 55 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Walter Roth
Keyword(s):  
Type Theorem ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Linear Operators ◽  
Weighted Spaces ◽  
Korovkin Type Theorem ◽  
Korovkin Type Approximation Theorem ◽  
Spaces Of Continuous Functions ◽  
Locally Convex Topologies ◽  
Locally Convex

We prove a Korovkin type approximation theorem for positive linear operators on weighted spaces of continuous real-valued functions on a compact Hausdorff space X. These spaces comprise a variety of subspaces of C (X) with suitable locally convex topologies and were introduced by Nachbin 1967 and Prolla 1977. Some early Korovkin type results on the weighted approximation of real-valued functions in one and several variables with a single weight function are due to Gadzhiev 1976 and 1980.

scholarly journals Korovkin-type theorems on $$B({\mathcal {H}})$$ and their applications to function spaces

2021 ◽  
Author(s):  
Wolfram Bauer ◽  
V. B. Kiran Kumar ◽  
Rahul Rajan
Keyword(s):  
Toeplitz Operators ◽  
Recent Literature ◽  
Fock Space ◽  
Banach Algebras ◽  
Type Theorem ◽  
Function Spaces ◽  
Korovkin Type Theorem ◽  
Type Approximation ◽  
Korovkin Type Theorems ◽  
Toeplitz Structure

AbstractWe prove Korovkin-type theorems in the setting of infinite dimensional Hilbert space operators. The classical Korovkin theorem unified several approximation processes. Also, the non-commutative versions of the theorem were obtained in various settings such as Banach algebras, $$C^{*}$$ C ∗ -algebras and lattices etc. The Korovkin-type theorem in the context of preconditioning large linear systems with Toeplitz structure can be found in the recent literature. In this article, we obtain a Korovkin-type theorem on $$B({\mathcal {H}})$$ B ( H ) which generalizes all such results in the recent literature. As an application of this result, we obtain Korovkin-type approximation for Toeplitz operators acting on various function spaces including Bergman space $$A^{2}({\mathbb {D}})$$ A 2 ( D ) , Fock space $$F^{2}({\mathbb {C}})$$ F 2 ( C ) etc. These results are closely related to the preconditioning problem for operator equations with Toeplitz structure on the unit disk $${\mathbb {D}}$$ D and on the whole complex plane $${\mathbb {C}}$$ C . It is worthwhile to notice that so far such results are available for Toeplitz operators on circle only. This also establishes the role of Korovkin-type approximation techniques on function spaces with certain oscillation property. To address the function theoretic questions using these operator theory tools will be an interesting area of further research.

Korovkin-type theorems and applications

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Nazim Mahmudov
Keyword(s):  
Type Theorem ◽  
Linear Operators ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Quantitative Results ◽  
Korovkin Type Theorems

AbstractLet {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.

scholarly journals A Voronovskaya-type theorem for a positive linear operator

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
Alexandra Ciupa
Keyword(s):  
Linear Operator ◽  
Exponential Growth ◽  
Positive Linear Operator ◽  
Type Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Voronovskaya Type Theorem

We consider a sequence of positive linear operators which approximates continuous functions having exponential growth at infinity. For these operators, we give a Voronovskaya-type theorem

THERMODYNAMIC FORMALISM FOR RANDOM TRANSFORMATIONS REVISITED

2008 ◽  
Vol 08 (01) ◽  
pp. 77-102 ◽  
Author(s):  
YURI KIFER
Keyword(s):  
Finite Type ◽  
Type Theorem ◽  
Thermodynamic Formalism ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Topological Mixing ◽  
Subshifts Of Finite Type

We return to the thermodynamic formalism constructions for random expanding in average transformations and for random subshifts of finite type with random rates of topological mixing, as well as to the Perron–Frobenius type theorem for certain random positive linear operators. Our previous expositions in [14, 19] and [21] were based on constructions which left some gaps and inaccuracies related to the measurability and uniqueness issues. Our approach here is based on Hilbert projective norms which were already applied in [5] for the thermodynamic formalism constructions for random subshifts of finite type but our method is somewhat different and more general so that it enables us to treat simultaneously both expanding and subshift cases.

scholarly journals THE ROLE OF DOMINATION AND SMOOTHING CONDITIONS IN THE THEORY OF EVENTUALLY POSITIVE SEMIGROUPS

2017 ◽  
Vol 96 (2) ◽  
pp. 286-298 ◽  
Author(s):  
DANIEL DANERS ◽  
JOCHEN GLÜCK
Keyword(s):  
Positive Operator ◽  
Type Theorem ◽  
Function Spaces ◽  
Linear Operators ◽  
The Other ◽  
Operator Semigroups ◽  
Positive Semigroups ◽  
Depth Study ◽  
The One

We carry out an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand, we prove that, on many important function spaces, they imply compactness properties. On the other hand, we show that these conditions can be omitted in a number of Perron–Frobenius type spectral theorems. We furthermore prove a Kreĭn–Rutman type theorem on the existence of positive eigenvectors and eigenfunctionals under certain eventual positivity conditions.

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