In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.
Soient la classe des cônes convexes saillants faiblement complets et la sous-classe de formée des cônes localement compacts de . Dans les dix dernières années, Alfsen, Bauer, Effros, Rogalski et Stormer ont donné de nombreuses propriétés équivalentes entre elles et qui caractérisent dans les cônes de Radon des mesures de Radon positives sur un espace compact . On montre ici que ces propriétés, convenablement interprétées, restent équivalentes dans la sous-classe des cônes presque bien...
Starting from Lagrange interpolation of the exponential function in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space . Given such a representable entire funtion , in order to study the approximation problem and the uniform convergence of these polynomials to on bounded sets of , we present a sufficient growth condition on the interpolating...
Let be a completely regular space, a boundedly complete vector lattice,