Locally Accretive Mappings in Banach Spaces
Claudio H. Morales · Bulletin of the London Mathematical Society · 1996
Let X be a real Banach space for which the closed unit ball has the fixed point property for nonexpansive self-mappings. Suppose that D is a bounded open subset of X, and T is a continuous mapping from the closure of D into X and locally accretive on D. Then T has a zero in D, provided that the following boundary condition is fulfilled: there exists an element z in D so that ‖Tz‖ < ‖Tx‖ for all x in the boundary of D.