When is the Optimal Domain of a Positive Linear Operator a Weighted L 1-space?

2009 ◽  
pp. 361-369
Author(s):  
Anton R. Schep
Keyword(s):  
Linear Operator ◽  
Positive Linear Operator ◽  
Optimal Domain

scholarly journals A Spline Group – Korovkin Approximation Theorem

2015 ◽  
Vol 7 (2) ◽  
pp. 110
Author(s):  
Malik Saad Al-Muhja
Keyword(s):  
Linear Operator ◽  
Approximation Theorem ◽  
Positive Linear Operator ◽  
Homogeneous Groups ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Korovkin Approximation ◽  
Korovkin Approximation Theorem

In this paper, using homogeneous groups, we prove a Korovkin type approximation theorem for a spline groupby using the notion of a generalization of positive linear operator.

Ratio and Stochastic Ergodic Theorems for Superadditive Processes

1979 ◽  
Vol 31 (2) ◽  
pp. 441-447 ◽  
Author(s):  
Humphrey Fong
Keyword(s):  
Linear Operator ◽  
Measure Space ◽  
Measure Zero ◽  
Positive Linear Operator ◽  
Finite Measure ◽  
Ergodic Theorems ◽  
Finite Measure Space ◽  
Image Position

1. Introduction. Let (X, , m) be a σ-finite measure space and let T be a positive linear operator on L1 = L1(X, , m). T is called Markovian if(1.1)T is called sub-Markovian if(1.2)All sets and functions are assumed measurable; all relations and statements are assumed to hold modulo sets of measure zero.For a sequence of L1+ functions (ƒ0, ƒ1, ƒ2, …), let(ƒn) is called a super additive sequence or process, and (sn) a super additive sum relative to a positive linear operator T on L1 if(1.3)and(1.4)

A Positive Linear Operator Using Probabilistic Approach

2006 ◽  
Vol 6 (12) ◽  
pp. 2662-2665 ◽  
Author(s):  
Ashok Sahai . ◽  
Shanaz Wahid . ◽  
Arvind Sinha .
Keyword(s):  
Linear Operator ◽  
Positive Linear Operator ◽  
Probabilistic Approach

scholarly journals Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yongfu Su
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Linear Operator ◽  
Nonexpansive Mapping ◽  
Error Estimate ◽  
Nonexpansive Mappings ◽  
Positive Linear Operator ◽  
Iteration Process ◽  
Iteration Algorithm ◽  
Iteration Sequence

The purpose of this article is to present a general viscosity iteration process{xn}which defined byxn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xnand to study the convergence of{xn}, whereTis a nonexpansive mapping andAis a strongly positive linear operator, if{αn},{βn}satisfy appropriate conditions, then iteration sequence{xn}converges strongly to the unique solutionx*∈f(T)of variational inequality〈(A−γf)x*,x−x*〉≥0,for allx∈f(T). Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given. The results presented in this paper extend, generalize, and improve the results of Xu, G. Marino and Xu and some others.

scholarly journals SOLUTION OF A NONLINEAR OPERATOR EQUATION OF THE FIRST KIND WITH A CONTINUOUS POSITIVE LINEAR OPERATOR

2021 ◽  
pp. 118-123
Author(s):  
I.A. Usenov ◽  
R.K. Usenova ◽  
A. Nurkalieva
Keyword(s):  
Hilbert Space ◽  
Exact Solution ◽  
Approximate Solution ◽  
Linear Operator ◽  
Operator Equation ◽  
Nonlinear Operator ◽  
Regularization Parameter ◽  
Positive Linear Operator ◽  
Nonlinear Operator Equation ◽  
The Right

In the space H, a nonlinear operator equation of the first kind is studied, when the linear, nonlinear operator and the right-hand side of the equation are given approximately. Based on the method of Lavrent'ev M.M. an approximate solution of the equation in Hilbert space is constructed. The dependence of the regularization parameter on errors was selected. The rate of convergence of the approximate solution to the exact solution of the original equation is obtained.

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>

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

scholarly journals The spectrum of an R-homomorphism

1977 ◽  
Vol 23 (1) ◽  
pp. 42-45 ◽  
Author(s):  
A. W. Wickstead
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Real Banach Space ◽  
Point Spectrum ◽  
Positive Linear Operator ◽  
Riesz Decomposition Property ◽  
Decomposition Property ◽  
Approximate Point Spectrum ◽  
Riesz Decomposition ◽  
The Riesz Decomposition Property

AbstractLet E be a real Banach space ordered by a closed, normal and generating cone. Suppose also that the order induced on E has the Riesz decomposition property. It is shown that if T:E → E is a positive linear operator with the property that y, z, a ∈ E with a ≧ Ty, Tz implies there is x ∈ E with x ≧ y, z and a ≧ Tx then the approximate point spectrum and spectrum of T are cyclic subsets of the complex plane. That is, if α = |α|γ lies in one of these sets then so does |α|γk for all integers k.

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.

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