We denote by 0 the set of all sequences u = (ux)k=1,2, = (u1, u2, ...) (uk E R) %3D satisfying sup Ju< 00. Moreover, we define a norm of as follows: I| = sup ul. Then, prove that is a Banach space with respect to || - ||- (It is sufficient to prove com- pleteness of , i.e., show that a Cauchy sequence {u}-1.2 is a convergent sequence in , where un) = (u", u",..) E e*.) %3D

We denote by 0 the set of all sequences u = (ux)k=1,2, = (u1, u2, ...) (uk E R) %3D satisfying sup Ju< 00. Moreover, we define a norm of as follows: I| = sup ul. Then, prove that is a Banach space with respect to || - ||- (It is sufficient to prove com- pleteness of , i.e., show that a Cauchy sequence {u}-1.2 is a convergent sequence in , where un) = (u", u",..) E e*.) %3D

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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