11. Let (V.||-|) be a normed vector space. Suppose e : V - R has the property that e(r+y) = 2r{r)e(s) for every r.y E l. Prove that if e is continuous at 0, then e is continuous at every r E V.
11. Let (V.||-|) be a normed vector space. Suppose e : V - R has the property that e(r+y) = 2r{r)e(s) for every r.y E l. Prove that if e is continuous at 0, then e is continuous at every r E V.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:11. Let (V. |1.|) be a normed vector space. Suppose e :V - R has the property that
e(r+y) = 2r(r)e(y) for every r.y El. Prove that if e is continuous at 0, then e is
continuous at every r€ V.
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