Results 141 to 150 of about 1,445 (159)

A-Statistical extension of the Korovkin type approximation theorem

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2005
The authors give a general Korovin type approximation theorem, using the concept of A-statistical convergence which is a regular summability method, which concerns the problem of approximating a function by means of a sequence of positive linear operators. One example is given.
Oktay Duman
exaly   +5 more sources

Note on a Korovkin-type theorem

Journal of Mathematical Analysis and Applications, 2014
A new Korovkin type theorem is established, giving a system of conditions which insures the convergence in \(C[0,1]\) of a sequence \((L_{n})_{n \geq 1}\) of positive linear operators to its limit operator denoted by \(L_{\infty}.\) The approximation error \(| L_{n}(f,x)-L_{\infty}(f,x) |,\) \(f \in C[0,1],\) \(x \in [0,1],\) is estimated by the first ...
Zoltán Finta
exaly   +3 more sources

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An abstract version of the Korovkin approximation theorem

Publicationes Mathematicae Debrecen, 2006
Using the \(A\)-statistical convergence, the authors establish first an analog of King's theorem, see \textit{J. P. King} [Acta Math. Hungar., 99, 203--208 (2003; Zbl 1027.41028)]. The main result of the paper is an abstract version of the Korovkin theorem, expressed in terms of statistical convergence. It is contained in Theorem 3.1.
Duman, Oktay, Orhan, Cihan
openaire   +3 more sources

Proofs of Korovkin's Theorems via Inequalities

The American Mathematical Monthly, 2003
correct answer (particularly for weaker contestants) seems a good idea. The author recently learned that Paul Coe of Dominican University announced similar results in his January 7, 2002 talk at the Joint Mathematics Meetings in San Diego. See http://www.ams.org/amsmtgs/2049_abstracts/973-tl-634.pdf for his talk announcement, dated September 15, 2001 ...
openaire   +2 more sources

A Korovkin type approximation theorem in statistical sense

Studia Scientiarum Mathematicarum Hungarica, 2006
In this study, using the concept of A-statistical convergence we investigate a Korovkin type approximation result for a sequence of positive linear operators defined on the space of all continuous real valued functions on any compact subset of the real m-dimensional space.
Duman, Oktay, Erkuş,Duman, Esra
openaire   +4 more sources

Korovkin’s Theorem for Functionals and Limits for Box Integrals

The American Mathematical Monthly, 2019
We prove a version of Korovkin’s theorem for functionals that is well suited to obtain limits for integrals of mean values and has applications to limits of certain box integrals.
Herzog, Gerd, Kunstmann, Peer Chr.
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Variations on a Theorem of Korovkin

The American Mathematical Monthly, 2006
Héctor E. Lomelí, César L. García
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Korovkin Theorems for Sequences of Contractions on LP-Spaces

1974
Ever since Korovkin published his celebrated theorem on the convergence of sequences of positive linear operators in 1953, it has been the study of numerous extensions and generalizations.
Hubert Berens, George G. Lorentz
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Statistical Convergence via q-Calculus and a Korovkin’s Type Approximation Theorem

Axioms, 2022
Mohammad Ayman Mursaleen, Stefano Serra Capizzano   +1 more
exaly  

Theorems of Korovkin and Stone-Weierstrass

1989
Let Δ = [a, b] be a closed interval in ℝ. The classical approximation theorem of Weierstrass (1885) asserts that any f ∈ C(Δ) can be approximated uniformly by polynomials, i.e., for any є > 0 there exists a polynomial Pє such that |f(x)–Pє (x) | < є holds for all x ∈ Δ.
openaire   +1 more source