Markov operators and n-copulas
We extend the definition of Markov operator in the sense of J. R. Brown and of earlier work of the authors to a setting appropriate to the study of n-copulas. Basic properties of this extension are studied.
We extend the definition of Markov operator in the sense of J. R. Brown and of earlier work of the authors to a setting appropriate to the study of n-copulas. Basic properties of this extension are studied.
The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.
We prove the existence of solutions to , together with appropriate boundary conditions, whenever is a maximal monotone graph in , for every fixed . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a rotation, for every fixed ; in other words, the graph is defined through , where is a Carathéodory contraction in . This definition is shown to be equivalent to the fact that is pointwise monotone...