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Task 18 Let (X, || - ||) be a Banach space, J CR be bounded and F C C'(J,X). If sup ||f(x)|| < o, ƒ€F, rEJ then F is uniformly equicontinuous in BC(J, X).

Task 18 Let (X, || - ||) be a Banach space, J CR be bounded and F C C'(J,X). If sup ||f(x)|| < o, ƒ€F, rEJ then F is uniformly equicontinuous in BC(J, X).

Advanced Engineering Mathematics
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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Task 18 Let (X, || - ||) be a Banach space, J CR be bounded and F C C'(J,X). If sup ||f(x)|| < o, ƒ€F, rEJ then F is uniformly equicontinuous in BC(J, X).
Transcribed Image Text:Task 18 Let (X, || - ||) be a Banach space, J CR be bounded and F C C'(J,X). If sup ||f(x)|| < o, ƒ€F, rEJ then F is uniformly equicontinuous in BC(J, X).
Task 12 Prove Lemmas 2.53, 2.54. Task 13 Let (M, d) be a compact metric space. Show that closed subsets of M are compact.
Transcribed Image Text:Task 12 Prove Lemmas 2.53, 2.54. Task 13 Let (M, d) be a compact metric space. Show that closed subsets of M are compact.
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