Locally Accretive Mappings in Banach Spaces | Zendy

Morales Claudio H. | Zendy

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Locally Accretive Mappings in Banach Spaces

Author(s) -

Morales Claudio H.

Publication year - 1996

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/28.6.627

Subject(s) - mathematics , banach space , unit sphere , bounded function , closure (psychology) , ball (mathematics) , pure mathematics , fixed point , boundary (topology) , discrete mathematics , mathematical analysis , economics , market economy

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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