BASIC PROPERTIES OF LINEAR RELATIVE n-WIDTHS

Sidorov, Sergei

doi:10.12732/ijpam.v96i4.10

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“…is equal to zero. Note that the case of linear operators preserving k-monotonicity was examined in [7].…”

Section: Introductionmentioning

confidence: 99%

On the order of approximation by linear shape-preserving operators on subsets of [0,1] with positive measure

Sidorov¹

2013

ijma

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Let Δ k denote the set of all k-monotone functions defined on [0,1]. Let 0 ≤ h < k be two integers and let σ = (σ 0 ,. .. , σ k) ∈ R k+1 , σ i ∈ {−1, 0, 1}, be such that σ h σ k = 0. Denote Δ h,k (σ) := ∩ k i=h σ i Δ i [0, 1]. Let r be such that h r < k, σ r = 0, σ r+1 = 0, σ r • σ r+2 = −1. This paper shows that if an approximation process {L n } n∈AE satisfies shapepreserving property L n (Δ h,k (σ)) ⊂ σ r Δ r , and the operators L n are assumed to be of finite rank n, then the order of convergence of D r L n f to D r f cannot be better than n −(k−r) even for functions 1, x,. .. , x k+2 , on any subset of [0,1] with positive measure.

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“…is equal to zero. Note that the case of linear operators preserving k-monotonicity was examined in [7].…”

Section: Introductionmentioning

confidence: 99%

On the order of approximation by linear shape-preserving operators on subsets of [0,1] with positive measure

Sidorov¹

2013

ijma

View full text Add to dashboard Cite

show abstract

BASIC PROPERTIES OF LINEAR RELATIVE n-WIDTHS

Abstract: The paper examines the basic properties of linear relative widths as well as the different ways of finding their estimates.

Cited by 1 publication

References 8 publications

On the order of approximation by linear shape-preserving operators on subsets of [0,1] with positive measure

On the order of approximation by linear shape-preserving operators on subsets of [0,1] with positive measure

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