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 (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 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 (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.

A Class of Positive Linear Operators

1968 ◽  
Vol 11 (1) ◽  
pp. 51-59 ◽  
Author(s):  
J. P. King
Keyword(s):  
Linear Operator ◽  
Linear Space ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Convergence Of Sequences

Let F[a, b] be the linear space of all real valued functions defined on [a, b]. A linear operator L: C[a, b] → F[a, b] is called positive (and hence monotone) on C[a, b] if L(f)≥0 whenever f≥0. There has been a considerable amount of research concerned with the convergence of sequences of the form {Ln(f)} to f where {Ln} is a sequence of positive linear operators on C[a, b].

scholarly journals On linear operators on ordered banach spaces

1983 ◽  
Vol 27 (2) ◽  
pp. 285-305 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Order Structure ◽  
Ordered Banach Space ◽  
Continuous Linear ◽  
Positive Unit ◽  
Ordered Banach Spaces ◽  
Continuous Linear Operators

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.

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.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

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