I am unable to solve these questions I want help in this. Task 18Let (X, || - ||) be a Banach space, J CR be bounded and F C C'(J,X). Ifsup ||f(x)|| < o,ƒ€F,rEJthen F is uniformly equicontinuous in BC(J, X). Task 12Prove Lemmas 2.53, 2.54.Task 13Let (M, d) be a compact metric space. Show that closed subsets of M are compact.

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Answered: Task 18 Let (X, || - ||) be a Banach…

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).