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Recently, Durante and Jaworski (2008) [6] have proved that the class of absolutely continuous copulas with a given diagonal section is non-empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null-measure. In this paper, we show that if we consider sub-diagonals (or super-diagonals),… (More)

We introduce a constructive method, by using a doubly stochastic measure, to describe all the copulas that, in view of Sklar's Theorem, are able to connect a bivariate distribution to its marginals. We use this to give the lower and upper optimal bounds for all the copulas that extend a given subcopula.

In recent years special attention has been devoted to the problem of finding a copula, the diagonal section and opposite diagonal section of which are known. For given diagonal function and opposite diagonal functions, we provide necessary and sufficient conditions for the existence of a copula to have these functions as diagonal and opposite diagonal… (More)

The aim of this paper is to show, using some of Barnsley's ideas, how it is possible to generalize a fractal interpolation problem to certain post critically finite (PCF) compact sets in R n. We use harmonic functions to solve this fractal interpolation problem.

We give a new approach to Taylor's remainder formula, via a generalization of Cauchy's generalized mean value theorem, which allows us to include the well-known Schölomilch, Lebesgue, Cauchy, and the Euler classic types, as particular cases.

In this paper we study a class of duality functions given by the solution of a system of functional equations related to the De Rham system. With the aid of a generalized dyadic representation system in the unit interval, we study a negation N which is a duality function for pairs of operators satisfying certain boundary conditions. New properties of N are… (More)

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