Volterra-Choquet nonlinear operators

Abstract

In this paper we study to what extent properties of the classical linear Volterra operators can be transferred to the nonlinear Volterra-Choquet operators, obtained by replacing the classical linear integral with respect to the Lebesgue measure, by the nonlinear Choquet integral with respect to a nonadditive set function. Compactness, Lipschitz and cyclicity properties are studied.