Displaying similar documents to “King type modification of q -Bernstein-Schurer operators”

Statistical approximation properties of q-Baskakov-Kantorovich operators

Vijay Gupta, Cristina Radu (2009)

Open Mathematics

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In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.

The fractional dimensional theory in Lüroth expansion

Luming Shen, Kui Fang (2011)

Czechoslovak Mathematical Journal

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It is well known that every x ∈ ( 0 , 1 ] can be expanded to an infinite Lüroth series in the form of x = 1 d 1 ( x ) + ⋯ + 1 d 1 ( x ) ( d 1 ( x ) - 1 ) ⋯ d n - 1 ( x ) ( d n - 1 ( x ) - 1 ) d n ( x ) + ⋯ , where d n ( x ) ≥ 2 for all n ≥ 1 . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets F φ = { x ∈ ( 0 , 1 ] : d n ( x ) ≥ φ ( n ) , ∀ n ≥ 1 } are completely determined, where φ is an integer-valued function defined on ℕ , and φ ( n ) → ∞ as n → ∞ .

On q-Szász-Durrmeyer operators

Nazim Mahmudov, Havva Kaffaoğlu (2010)

Open Mathematics

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In the present paper, we introduce the q-Szász-Durrmeyer operators and justify a local approximation result for continuous functions in terms of moduli of continuity. We also discuss a Voronovskaya type result for the q-Szász-Durrmeyer operators.