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Approximation of Univariate Set-Valued Functions - an Overview

Dyn, Nira, Farkhi, Elza, Mokhov, Alona (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.The paper is an updated survey of our work on the approximation of univariate set-valued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact convex images we use Minkowski...

Approximations and error bounds for computing the inverse mapping

Lucas Jódar, Enrique Ponsoda, G. Rodríguez Sánchez (1997)

Applications of Mathematics

In this paper we propose a procedure to construct approximations of the inverse of a class of 𝒞 m differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.

Area functionals and Godbillon-Vey cocycles

Takashi Tsuboi (1992)

Annales de l'institut Fourier

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the topology...

Arrow-Hahn economic models with weakened conditions of continuity

Inese Bula, Dace Rika (2006)

Banach Center Publications

In this article we give descriptions of some economic models that are based on Arrow-Hahn economic model. Finally we consider a model with two major assumptions: first, there is discontinuous excess demand function and, second, if price goes to zero, then it is possible that excess demand may approach infinity. For this last new economic model the existence of quasi-equilibrium is proved.

Associative n -dimensional copulas

Andrea Stupňanová, Anna Kolesárová (2011)

Kybernetika

The associativity of n -dimensional copulas in the sense of Post is studied. These copulas are shown to be just n -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.

Asymmetric covariance estimates of Brascamp–Lieb type and related inequalities for log-concave measures

Eric A. Carlen, Dario Cordero-Erausquin, Elliott H. Lieb (2013)

Annales de l'I.H.P. Probabilités et statistiques

An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the L 2 norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto [Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential....

Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

Jaroslav Jaroš, Kusano Takaŝi, Jelena Manojlović (2013)

Open Mathematics

Positive solutions of the nonlinear second-order differential equation ( p ( t ) | x ' | α - 1 x ' ) ' + q ( t ) | x | β - 1 x = 0 , α > β > 0 , are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

Currently displaying 701 – 720 of 4562