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Bulletin of the London Mathematical Society 1996 28(6):627-633; doi:10.1112/blms/28.6.627
© 1996 by London Mathematical Society
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© London Mathematical Society

Locally Accretive Mappings in Banach Spaces

Claudio H. Morales

Department of Mathematics University of Alabama in Huntsville Huntsville, AL 35899 USA

Received 29 March 1995.

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.


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