- G A Normed Vector Space V Is Strictly Convex If Kuk Kvk K U V 2k 1 For Vectors U V V Implies That U V A 1 (36.03 KiB) Viewed 46 times
G. A normed vector space V is strictly convex if kuk = kvk = k(u + v)/2k = 1 for vectors u,v ∈ V implies that u = v. (a)
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G. A normed vector space V is strictly convex if kuk = kvk = k(u + v)/2k = 1 for vectors u,v ∈ V implies that u = v. (a)
G. A normed vector space V is strictly convex if kuk = kvk = k(u + v)/2k = 1 for vectors u,v ∈ V implies that u = v. (a) Show that an inner product space is always strictly convex. (b) Show that R2 with the norm k(x,y)k∞ = max{|x|,|y|} is not strictly convex.
G. A normed vector space V is strictly convex if ||u|| = ||v|| = ||(u+v)/2|| = 1 for vectors u, v E V implies that u = v. (a) Show that an inner product space is always strictly convex. (b) Show that R² with the norm ||(x,y) ||∞ = max{|x], [y]} is not strictly convex.
G. A normed vector space V is strictly convex if ||u|| = ||v|| = ||(u+v)/2|| = 1 for vectors u, v E V implies that u = v. (a) Show that an inner product space is always strictly convex. (b) Show that R² with the norm ||(x,y) ||∞ = max{|x], [y]} is not strictly convex.