||PA(x) – PA(Y)||< ||x – y|l: A(y)||

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 31.
Let H be a Hilbert space and ACHA closed convex non-empty set. Prove that
РА: Н — Н is non-ezpansive, і.е.,
||PA(x) – PA(Y)|| < ||r – y||, Væ, y E H.
(Ра is the orthoдопal projection оп A).
Transcribed Image Text:Problem 31. Let H be a Hilbert space and ACHA closed convex non-empty set. Prove that РА: Н — Н is non-ezpansive, і.е., ||PA(x) – PA(Y)|| < ||r – y||, Væ, y E H. (Ра is the orthoдопal projection оп A).
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