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Displaying 81 – 100 of 115

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Generalized weighted quasi-arithmetic means and the Kolmogorov-Nagumo theorem

Janusz Matkowski (2013)

Colloquium Mathematicae

A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions f , . . . , f k : I , k ≥ 2, denoted by A [ f , . . . , f k ] , is considered. Some properties of A [ f , . . . , f k ] , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For a sequence of...

Generalized α-variation and Lebesgue equivalence to differentiable functions

Jakub Duda (2009)

Fundamenta Mathematicae

We find conditions on a real function f:[a,b] → ℝ equivalent to being Lebesgue equivalent to an n-times differentiable function (n ≥ 2); a simple solution in the case n = 2 appeared in an earlier paper. For that purpose, we introduce the notions of C B V G 1 / n and S B V G 1 / n functions, which play analogous rôles for the nth order differentiability to the classical notion of a VBG⁎ function for the first order differentiability, and the classes C B V 1 / n and S B V 1 / n (introduced by Preiss and Laczkovich) for Cⁿ smoothness. As a consequence,...

Generators for algebras dense in L p -spaces

Alexander J. Izzo, Bo Li (2013)

Studia Mathematica

For various L p -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in L p ( μ ) . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...

Generic chaos

Ľubomír Snoha (1990)

Commentationes Mathematicae Universitatis Carolinae

Currently displaying 81 – 100 of 115