Generalized Volterra integral equations
Generalized weighted quasi-arithmetic means and the Kolmogorov-Nagumo theorem
A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions , k ≥ 2, denoted by , is considered. Some properties of , 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
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 and 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 and (introduced by Preiss and Laczkovich) for Cⁿ smoothness. As a consequence,...
Generalized -Newton inequalities revisited.
Generalizing the arithmetic geometric mean - a hapless computer experiment.
Generating functions for the mean value of a function on a sphere and its associated ball in .
Generators for algebras dense in -spaces
For various -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 . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...
Generic chaos
Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities
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.
Geometric convexity of a function involving gamma function and applications to inequality theory.
Geometric expansion, Lyapunov exponents and foliations
Geometrical convexity and generalizations of the Bohr-Mollerup theorem on the gamma function.
Géométrie des polynômes. Coût global moyen de la méthode de Newton
Geometrische Bedingungen für die Integrabilität von Vektor-Feldern auf Teilmengen.
Geometrische und analytische Untersuchung der Weierstrassschen Function.
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
Giving lectures on nonstandard analysis. (Lire l'analyse non standard.)
Global behavior of integral transforms.
Global regularity for solutions of the minimal surface equation with continuous boundary values
Global smoothness preservation and the variation-diminishing property.