Assume that f is an increasing function satisfying the recurrence relation f (n) = af (n∕b) + cnd, where a ≥ 1, b is an integer greater than 1, and c and d are positive real numbers Show that if a < bd, then f (n) is O(nd).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Assume that f is an increasing function satisfying the recurrence relation f (n) = af (n∕b) + cnd, where a ≥ 1, b is an integer greater than 1, and c and d are positive real numbers

Show that if a < bd, then f (n) is O(nd).

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