Convexity and Notions of Nonexpansiveness
Heinz H. Bauschke, Patrick L. Combettes · CMS books in mathematics · 2017
Nonexpansive operators are Lipschitz continuous operators with Lipschitz constant 1. They play a central role in applied mathematics because many problems in nonlinear analysis reduce to finding fixed points of nonexpansive operators. In this chapter, we discuss nonexpansiveness and several variants. The properties of the fixed point sets of nonexpansive operators are investigated, in particular in terms of convexity.