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Thursday, July 23, 2020 | History

9 edition of Extension of positive operators and Korovkin theorems found in the catalog. # Extension of positive operators and Korovkin theorems

## by Klaus Donner

Written in English

Subjects:
• Linear operators.,
• Positive operators.,
• Banach lattices.,
• Convergence.

• Edition Notes

Classifications The Physical Object Statement Klaus Donner. Series Lecture notes in mathematics ;, 904, Lecture notes in mathematics (Springer-Verlag) ;, 904. LC Classifications QA3 .L28 no. 904, QA329.2 .L28 no. 904 Pagination xii, 181 p. : Number of Pages 181 Open Library OL3782970M ISBN 10 0387111832 LC Control Number 81023304

Approximation theory. Korovkin type approximation theorems are practical tools to check whether a given sequence (A n) n≥1 of positive linear operators on C[a, b] of all continuous functions on the real interval [a, b] is an approximation process. That is, these theorems present a variety of test functions which provide that the approximation property holds on the whole space if it holds for 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 weighted L p spaces, 1 ≤ p theorems by means of 풜-summability which is a stronger convergence

sequence of positive linear operators that map C(Ω) into itself. We establish two Korovkin-type theorems in which the limit of the sequence of operators is not necessarily the identity. 1. Introduction and Notation Let C[a,b] be the linear space of all real-valued continuous functions on [a,b] and let T be a linear operator which maps C[a,b Simplicial cones and the existence of shape-preserving cyclic operators. [Rocky Mountain J. Math. 28 () (3) ] that, under certain conditions on S *, P =I n admits a shape-preserving extension if and only if S * K. DonnerExtension of Positive Operators and Korovkin Theorems. Springer-Verlag, New York () Google Scholar

Abstract. This paper is devoted to studying weighted A-statistical convergence and statistical weighted A-summability of fuzzy sequences and their representations of sequences of λ-levels, which are obtain necessary and sufficient conditions for the matrix A to be weighted fuzzy regular and derive some inclusion relations concerning these newly proposed ://   of Korovkin type theorems is really huge, a search on Google oﬀering more t results. However, except for Theorem in the paper of Bauer , the extension of this theory beyond the framework of linear functional analysis remained largely unexplored. Inspired by the Choquet theory of integrability with respect to a nonadditive

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### Extension of positive operators and Korovkin theorems by Klaus Donner Download PDF EPUB FB2

Extension of Positive Operators Extension of positive operators and Korovkin theorems book Korovkin Theorems. Authors; Klaus Donner; Search within book.

Front Matter. Pages I PDF. Cone embeddings for vector lattices A vector-valued Hahn-Banach theorem. Klaus Donner.

Pages Bisublinear and subbilinear functionals. Klaus Donner. Pages Extension of L 1-valued positive operators Cone embeddings for vector lattices.- A vector-valued Hahn-Banach theorem.- Bisublinear and subbilinear functionals.- Extension of L1-valued positive operators.- Extension of positive operators in Lp-spaces.- The Korovkin closure for equicontinuous nets of positive operators.- Korovkin theorems for the identity mapping on classical Banach Cone embeddings for vector lattices --A vector-valued Hahn-Banach theorem --Bisublinear and subbilinear functionals --Extension of L1-valued positive operators --Extension of positive operators in Lp-spaces --The Korovkin closure for equicontinuous nets of positive operators --Korovkin theorems for the identity mapping on classical Banach COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus Extension of positive operators and Korovkin theorems Klaus Donner （Lecture notes in mathematics, ） Springer-Verlag, Berlin: New Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link) Cite this chapter as: Donner K.

() Extension of L 1-valued positive : Extension of Positive Operators and Korovkin Theorems. Lecture Notes in Mathematics, vol Extension of Positive Operators and Korovkin Theorems pp Donner K. () Bisublinear and subbilinear functionals. In: Extension of Positive Operators and Korovkin Theorems.

Lecture Notes in Mathematics, vol Springer, Berlin, ://   Donner K. () Korovkin theorems for the identity mapping on classical Banach lattices. In: Extension of Positive Operators and Korovkin Theorems.

Lecture Notes in Mathematics, vol   The Korovkin theorems are simple yet powerful tools for deciding whether a given sequence of positive linear operators on or is an approximation process.

Furthermore, they have been the source of a considerable amount of research in several other fields of mathematics (cf. Korovkin-type approximation theory).

1 day ago  K. Donner, "Extension of positive operators and Korovkin theorems", Lecture Notes in Mathematics,Springer () [a6] P.P. Korovkin, "On convergence of linear positive operators in the space of continuous functions" Dokl. Akad. Nauk. SSSR, 90 () pp. – (In Russian) [a7] The classical Korovkin type theorems provide conditions for whether a given sequence of positive linear operators converges to the identity operator in the space of continuous functions on a   5 Korovkin-type theorems for positive linear operators 6 Korovkin-type theorems for the identity operator in C0(X) 7 Korovkin-type theorems for the identity operator on C(X), X compact Surveys in Approximation Theory Volume 5, pp.

92– c Surveys in Approximation Theory. ISSN (The nonlinear extension of Korovkin’s theorem: the several variables case) Suppose that X is a loc ally compact subset of the Euclide an space R N and E is a vector sublattic e of F (X) that 's.

K. Donner, "Extension of positive operators and Korovkin theorems", Lecture Notes in Mathematics,Springer () [a6] P.P. Korovkin, "On convergence of linear positive operators in the space of continuous functions" Dokl.

Akad. Nauk. SSSR, 90 () pp. – (In Russian) [a7] Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln)n≥1 of positive linear operators on C[0,1] of all continuous functions on the real interval [0,1] is 's_Theorem.

Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval is an approximation :// Triangular A-Statistical Approximation by Double Sequences of Positive Linear Operators we study an extension to non-positive operators.

the classical Korovkin theorems and their lacunary JOURNAL OF APPROXIMATION THEORY 1, () Convergence of Operators and Korovkin's Theorem1 DANIEL E. WULBERT Department of Mathematics^ University of Washington, Seattle, Washington I. INTRODUCTION AND NOTATION LetL, denote a sequence of operators defined on C[0,1] (C^, respectively).

Originating from Korovkin's theorems (cf. Korovkin theorems), this theory consists of a collection of results whose main objective is to investigate under what circumstances the convergence of a (particular) sequence (more generally, net) of linear operators acting on a topological vector space is, in fact, a consequence of its convergence on special (possibly finite) ://.

In this paper, we propose to introduce a new Λ 2-weighted statistical upon this definition, we prove some Korovkin type theorems. We also find the rate of the convergence for this kind of weighted statistical convergence and derive some Voronovskaya type ://In particular,\ud we show that, if M is a subset of C0 (X) that separates the\ud points of X and if f0 in C0(X) is strictly positive, then\ud f0,f 0 M, f0 M2 is a Korovkin set in C0(X).\ud \ud This result is very useful because it furnishes a simple way to\ud construct Korovkin sets, but in addition, as we show in Section 9,\ud it turns out JOURNAL OF APPROXIMATION THE () Korovkin Closures for Positive Linear Operators KLAUS DONNER Mathematisches Institut der Universit Erlangen-Nurnberg, D Ericingen, West Germany Communicated by G.

G. Lorentz Received Novem INTRODUCTION Let E and F be topological vector lattices, and let H denote a linear subspace of ://