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Displaying 81 – 100 of 115

Generalized Volterra integral equations

Štefan Schwabik (1982)

Czechoslovak Mathematical Journal

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 $f ₁, . . ., f_{k} : I \to ℝ$ , k ≥ 2, denoted by $A^{[f ₁, . . ., f_{k}]}$ , is considered. Some properties of $A^{[f ₁, . . ., f_{k}]}$ , 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,...

Generalized $λ$ -Newton inequalities revisited.

Xu, Jianhong (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Generalizing the arithmetic geometric mean - a hapless computer experiment.

Peetre, Jaak (1989)

International Journal of Mathematics and Mathematical Sciences

Generating functions for the mean value of a function on a sphere and its associated ball in $ℝ^{n}$ .

Toma, Antonela (2008)

Journal of Inequalities and Applications [electronic only]

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

Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities

Tomasz Bielaczyc (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that for a typical continuous learning system defined on a compact convex subset of ℝⁿ the Hausdorff dimension of its invariant measure is equal to zero.