A differential equation approach for solving implicit state-dependent convex sweeping processes in Banach spaces

Abstract

In the setting of 2-uniformly convex Banach spaces, we prove the existence of solutions for a variant of the implicit state-dependent convex sweeping processes. Our approach is based on a differential equation associated with the generalized projection operator.

Keywords

• uniformly smooth and uniformly convex banach spaces
• differential equations
• implicit convex sweeping process
• generalized projection
• duality mapping