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

AIMS MATHEMATICS（2024）

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摘要

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.

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关键词

uniformly smooth and uniformly convex Banach spaces,differential equations,implicit convex sweeping process,generalized projection,duality mapping

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