Volterra-Choquet nonlinear operators

Sorin G. Gal

DOI: http://dx.doi.org/10.12775/TMNA.2020.009

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.

Keywords


Choquet integral; monotone; submodular and continuous from below set function; Choquet $L^{p}$-space; distorted Lebesgue measures; Volterra-Choquet nonlinear operator; compactness; Lipschitz properties; cyclicity

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