Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf .. ... d1 + + An + An ... for any n points x1, ..., x, in I and any positive numbers A1, An. ....
Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf .. ... d1 + + An + An ... for any n points x1, ..., x, in I and any positive numbers A1, An. ....
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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Transcribed Image Text:Suppose that f (x) is convex and continuous on an interval I. Show that
x1 +·+ A„xn
+ An
dif(x1) + · ·· + Anf(xn)
A1 +...+ An
..
for any n points x1, ...,
X, in I and any positive numbers A1,
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