Let (Jn)neN be a sequence of functions f: R → R satisfying|fn+1(c) – fn(c)|< a\fn(c) – fn-1(c)[for n > 2 and neN , and ae(0, 1). Prove that (Sn)n€N isa pointwise convergent sequence of functions at x = c.

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Answered: Let (Jn)neN be a sequence of functions…

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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Let (Jn)neN be a sequence of functions f: R → R satisfying |fn+1(c) – fn(c)|< a\fn(c) – fn-1(c)[for n > 2 and neN , and ae(0, 1). Prove that (Sn)n€N is a pointwise convergent sequence of functions at x = c.