Weighted approximation by Baskakov-type operators

Ivanov, Kamen; Parvanov, Parvan E.

doi:10.1007/s10474-011-0135-x

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The Case C =1

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Cited by 4 publications

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“…The direct and strong converse results are known also in this case (see [11], Theorem 1.2, Theorem 1.3 and [12], Theorem 1.1):…”

Section: The Case C =mentioning

confidence: 92%

Strong Converse Results for Linking Operators and Convex Functions

Acu

Heilmann

Raşa

2020

Journal of Function Spaces

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We consider a family B n , ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n , c and a fixed convex function f , B n , ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n , ρ c applied to convex functions.

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“…The direct and strong converse results are known also in this case (see [11], Theorem 1.2, Theorem 1.3 and [12], Theorem 1.1):…”

Section: The Case C =mentioning

confidence: 92%