1,720,991 research outputs found
A Sequence of Kantorovich-Type Operators on Mobile Intervals
No full textIn this paper, we introduce and study a new sequence of positive linear operators, acting on both
spaces of continuous functions as well as spaces of integrable functions on [0; 1]. We state some qualitative properties
of this sequence and we prove that it is an approximation process both in C([0; 1]) and in Lp([0; 1]), also providing
some estimates of the rate of convergence. Moreover, we determine an asymptotic formula and, as an application,
we prove that certain iterates of the operators converge, both in C([0; 1]) and, in some cases, in Lp([0; 1]), to a limit
semigroup. Finally, we show that our operators, under suitable hypotheses, perform better than other existing ones in
the literature
On the approximation properties of generalized Gamma-type operators in several function spaces
No full textIn the present paper, we study a class of integral operators of probabilistic type, which are constructed by means of the generalized Gamma distribution. In particular, we discuss their approximation properties in weighted continuous function spaces and Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}L<^>p\end{document}-spaces, providing some estimates of the rate of convergence by means of different moduli of smoothness as well as an asymptotic formula. The paper concludes with some illustrative examples
On some representation formulae for operator semigroups in terms of integrated means
Full text linkThe aim of the paper is to develop some representation formulae for strongly continuous operator
semigroups on Banach spaces, in terms of limits of integrated means with respect to some given family
of probability Borel measures and other parameters.
The cases where these limits hold true pointwise or uniformly on compact subintervals are discussed
separately. In order to face them different methods have been required: the former case has been
studied by using purely functional-analytic methods, the latter one by involving methods arising from
Approximation Theory.
The paper also contains some estimates of the rate of convergence in terms of the rectified modulus of
continuity and the second modulus of continuity.
In a final section some illustrative examples and applications are provided
On the traction problem for steady elastic oscillations equations: the double layer potential ansatz
Full text linkThe three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means of a double layer potential is considered instead of the more usual simple layer potential
Kantorovich-type modifications of certain discrete-type operators on the positive real axis
No full textThe paper is concerned with the approximation properties of a modification of Kantorovich-type of a general class of operators of discrete-type. Such a modification was introduced by Agratini in 2015; in particular, we focus on extending its approximation properties in several function spaces, including polynomial weighted spaces of any degree as well as Lp-spaces. Some estimates of the rate of convergence are also obtained
On a generalization of Szász-Mirakjan-Kantorovich operators
No full textIn this paper we introduce and study a sequence of
positive linear operators acting on suitable spaces of measurable
functions on [0, +\infty[, including L^p([0, +\infty[) spaces,
1 \leq p <+\infty, and continuous function spaces with polynomial
weights. These operators generalize the
Sz\'{a}sz-Mirakjan-Kantorovich operators and they allow to
approximate (or to reconstruct) suitable measurable functions by
knowing their mean values on a sequence of subintervals of [0,+\infty[ that do not constitute a subdivision of it. We also give
some estimates of the rates of convergence by means of suitable
moduli of smoothness
On the approximation properties of generalized Gamma-type operators in several function spaces
No full textIn the present paper we study a class of integral operators of probabilistic type, which are constructed by means of the generalized Gamma distribution. In particular, we discuss their approximation properties in weighted continuous functions spaces and Lp-spaces, providing some estimates of the rate of convergence by means of different moduli of smoothness as well as an asymptotic formula. The paper concludes with some illustrative examples
- …
