Continuity properties of projection operators | Zendy

JeanPaul Penot | Zendy

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Continuity properties of projection operators

Author(s) -

JeanPaul Penot

Publication year - 2005

Publication title -

journal of inequalities and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.735

H-Index - 50

eISSN - 1029-242X

pISSN - 1025-5834

DOI - 10.1155/jia.2005.509

Subject(s) - mathematics , projection (relational algebra) , modulus of continuity , banach space , regular polygon , uniformly convex space , bounded function , uniform continuity , uniform boundedness , operator (biology) , pure mathematics , bounded operator , point (geometry) , mathematical analysis , type (biology) , geometry , eberlein–šmulian theorem , lp space , metric space , ecology , biochemistry , chemistry , algorithm , repressor , gene , transcription factor , biology

We prove that the projection operator on a nonempty closed convex subset Open image in new window of a uniformly convex Banach spaces is uniformly continuous on bounded sets and we provide an estimate of its modulus of uniform continuity. We derive this result from a study of the dependence of the projection on Open image in new window of a given point when Open image in new window varies.

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