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

Taylor's formula and preservation of generalized convexity for positive linear operators

2000 ◽  
Vol 37 (3) ◽  
pp. 765-777 ◽  
Author(s):  
José A. Adell ◽  
Alberto Lekuona
Keyword(s):  
Generalized Convexity ◽  
Positive Linear Operator ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Birth Process ◽  
Absolutely Continuous Functions ◽  
Taylor’S Formula ◽  
Differentiable Functions ◽  
Taylor's Formula

In this paper, we consider positive linear operators L representable in terms of stochastic processes Z having right-continuous non-decreasing paths. We introduce the equivalent notions of derived operator and derived process of order n of L and Z, respectively. When acting on absolutely continuous functions of order n, we obtain a Taylor's formula of the same order for such operators, thus extending to a positive linear operator setting the classical Taylor's formula for differentiable functions. It is also shown that the operators satisfying Taylor's formula are those which preserve generalized convexity of order n. We illustrate the preceding results by considering discrete time processes, counting and renewal processes, centred subordinators and the Yule birth process.

scholarly journals Generalized Kantorovich modifications of positive linear operators

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ana-Maria Acu ◽  
Ioan Cristian Buscu ◽  
Ioan Rasa
Keyword(s):  
Linear Operator ◽  
Generalized Convexity ◽  
Invariant Measures ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Voronovskaya Formula

<p style='text-indent:20px;'>Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized convexity, invariant measures and iterates. Some known results from the literature are extended.</p>

Taylor's formula and preservation of generalized convexity for positive linear operators

2000 ◽  
Vol 37 (03) ◽  
pp. 765-777 ◽  
Author(s):  
José A. Adell ◽  
Alberto Lekuona
Keyword(s):  
Generalized Convexity ◽  
Positive Linear Operator ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Birth Process ◽  
Absolutely Continuous Functions ◽  
Taylor’S Formula ◽  
Differentiable Functions ◽  
Taylor's Formula

In this paper, we consider positive linear operators L representable in terms of stochastic processes Z having right-continuous non-decreasing paths. We introduce the equivalent notions of derived operator and derived process of order n of L and Z, respectively. When acting on absolutely continuous functions of order n, we obtain a Taylor's formula of the same order for such operators, thus extending to a positive linear operator setting the classical Taylor's formula for differentiable functions. It is also shown that the operators satisfying Taylor's formula are those which preserve generalized convexity of order n. We illustrate the preceding results by considering discrete time processes, counting and renewal processes, centred subordinators and the Yule birth process.

scholarly journals The iterates of positive linear operators with the set of constant functions as the fixed point set

2016 ◽  
Vol 32 (2) ◽  
pp. 165-172
Author(s):  
TEODORA CATINAS ◽  
◽  
DIANA OTROCOL ◽  
IOAN A. RUS ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Linear Operator ◽  
Banach Lattice ◽  
Nonempty Subset ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Fixed Point Set ◽  
Real Functions ◽  
Point Set

Let Ω ⊂ Rp, p ∈ N∗ be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A. Some relevant examples are also given.

Approximation by mixed positive linear operators based on second-kind beta transform

2021 ◽  
Author(s):  
Naokant Deo ◽  
Ram Pratap
Keyword(s):  
Bounded Variation ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Functions Of Bounded Variation ◽  
Approximation Operators ◽  
Voronovskaya Type Theorem ◽  
Mixed Approximation ◽  
Direct Results

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

scholarly journals Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shahid Ahmad Wani ◽  
M. Mursaleen ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Order Of Convergence ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem

AbstractIn this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

scholarly journals BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

2007 ◽  
Vol 49 (1) ◽  
pp. 145-154
Author(s):  
BRUCE A. BARNES
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Integral Operators ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions

Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

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