that the triangle Prove axiom vom for a with the the closed the defination is eqquivalent norm Convewity of unit b'all. More precisely, if X is on which function linear Space is given with the properDies, P(Ax)= P(x) xEX,dEK then and only if Bz = 9x€Xlp(z)s 4] norm if is Convex.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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4. Prove
axiom vom
for
that the triangle.
the defination
is eqguivalent
Converity of
Hor a
noim
nith the
the closed
Unit ball.
precisely, if X is
Space
function
More
linear
on which
is
given a
with the
proper Dies,
P(Ax)= P(x) xEX, Y dEIK
then
and only if bx= jx€Xlp(z) < 4]
is
norm if
%3D
is
Convex.
Transcribed Image Text:4. Prove axiom vom for that the triangle. the defination is eqguivalent Converity of Hor a noim nith the the closed Unit ball. precisely, if X is Space function More linear on which is given a with the proper Dies, P(Ax)= P(x) xEX, Y dEIK then and only if bx= jx€Xlp(z) < 4] is norm if %3D is Convex.
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