Displaying similar documents to “On the concept of optimality interval.”

Continued fractions and the Gauss map.

Bates, Bruce, Bunder, Martin, Tognetti, Keith (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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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 coefficient inequalities in the Carathéodory class of functions

Adam Lecko (2000)

Annales Polonici Mathematici

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Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.