Some results on the space of bounded second κ-variation functions

Abstract

In this paper, we prove that if a globally Lipschitz non-autonomous superposition operator maps the space of functions of bounded second $ \kappa $-variation into itself then its generator function satisfies a Matkowski condition. We also provide conditions for the existence and uniqueness of solutions of the Hammerstein and Volterra equations in this space.

Keywords

• superposition operator
• integral equation
• bounded second $ \kappa $-variation
• hammerstein
• hammerstein-volterra
• volterra existence and uniqueness