Quantitative theorems on linear approximation processes of convolution operators in Banach spaces

Nishishiraho, Toshihiko

doi:10.2748/tmj/1178229498

Cited by 18 publications

(16 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Replacing the ordinary convergence by A-summability some approximation results have been studied in [15], [16], [18]. In the present paper, using A-summability we give an analog of Theorem A for a sequence of positive linear operators mapping the weighted space C ρ1 into the weighted B ρ2 .…”

Section: Matrix Summability and Positive Linear Operators 389mentioning

confidence: 91%

Matrix Summability and Positive Linear Operators

Atlıhan

Orhan

2007

Positivity

View full text Add to dashboard Cite

show abstract

Section: Matrix Summability and Positive Linear Operators 389mentioning

confidence: 91%

Matrix Summability and Positive Linear Operators

Atlıhan

Orhan

2007

Positivity

View full text Add to dashboard Cite

show abstract

“…The error of the Fejer's approximation Φ n * f −f in the uniform norm is investigated in many works: [9], [30], [40], pp. 339 -341, [41] etc.…”

Section: )mentioning

confidence: 99%

Problem of Estimation of Fractional Derivative for a Spectral Function of Gaussian Stationary Processes

Ostrovsky¹,

Sirota²

2015

Preprint

View full text Add to dashboard Cite

We study the problem of nonparametric estimation of the fractional derivative of unknown spectral function of Gaussian stationary sequence (time series) and show that these problems is well posed with the classical speed of convergence when the order of derivative is less than 0.5.We prove also the asymptotical unbiaseness and normality of offered estimates with optimal speed of convergence.For the construction of the confidence region in some functional norm we establish the Central Limit Theorem in correspondent space of continuous functions for offered estimates.

show abstract

“…), and a (n) k j = 0 otherwise, then A-summability reduces to almost convergence [8]. Some unification on Korovkin-type results through the use of a matrix summability method may be found in [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 96%