On approximation of functions by certain operators preserving $x^2$

Lucyna Rempulska; Karolina Tomczak

Displaying similar documents to “On approximation of functions by certain operators preserving $x^{2}$ ”

On the non-commutative neutrix product $ln x_{+} \circ x_{+}^{- s}$

Brian Fisher, Adem Kiliçman, Blagovest Damyanov, J. C. Ault (1996)

Commentationes Mathematicae Universitatis Carolinae

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The non-commutative neutrix product of the distributions $ln x_{+}$ and $x_{+}^{- s}$ is proved to exist for $s = 1, 2, ...$ and is evaluated for $s = 1, 2$ . The existence of the non-commutative neutrix product of the distributions $x_{+}^{- r}$ and $x_{+}^{- s}$ is then deduced for $r, s = 1, 2, ...$ and evaluated for $r = s = 1$ .

Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind

Barnabás Bede, Lucian Coroianu, Sorin G. Gal (2010)

Commentationes Mathematicae Universitatis Carolinae

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Starting from the study of the Shepard nonlinear operator of max-prod type in (Bede, Nobuhara et al., 2006, 2008), in the book (Gal, 2008), Open Problem 5.5.4, pp. 324–326, the Bleimann-Butzer-Hahn max-prod type operator is introduced and the question of the approximation order by this operator is raised. In this paper firstly we obtain an upper estimate of the approximation error of the form $ω_{1} (f; {(1 + x)}^{\frac{3}{2}} \sqrt{x / n})$ . A consequence of this result is that for each compact subinterval $[0, a]$ , with arbitrary $a > 0$ , the...

Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Xinxing Wu (2014)

Czechoslovak Mathematical Journal

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During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator $B_{w}^{n} : λ_{p} (A) \to λ_{p} (A)$ defined on the Köthe sequence space $λ_{p} (A)$ exhibits distributional $ϵ$ -chaos for any $0 < ϵ < diam λ_{p} (A)$ and any $n \in ℕ$ is obtained. Under this assumption, the principal measure of $B_{w}^{n}$ is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional $ϵ$ -chaos for any...

Approximation of bounded variation functions by a Bézier variant of the Bleimann, Butzer, and Hahn operators.

Gupta, Vijay, Doğru, Ogün (2006)

International Journal of Mathematics and Mathematical Sciences

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A Korovkin type approximation theorems via $ℐ$ -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

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Using the concept of $ℐ$ -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

Displaying similar documents to “On approximation of functions by certain operators preserving x 2 ”

On the non-commutative neutrix product ln x + ∘ x + - s

Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind

Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Approximation of bounded variation functions by a Bézier variant of the Bleimann, Butzer, and Hahn operators.

A Korovkin type approximation theorems via ℐ -convergence

Displaying similar documents to “On approximation of functions by certain operators preserving $x^{2}$ ”

On the non-commutative neutrix product $ln x_{+} \circ x_{+}^{- s}$

A Korovkin type approximation theorems via $ℐ$ -convergence