Under the condition that the unit ball has sufficiently many extreme points, every 2-local nonlinear surjective isometry on a normed space is affine.
Fundamentals of the the ory of operator algebras. Vol. II
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On 2-local nonlinear surjective isometries on normed spaces and C$^*$-algebras
Under the condition that the unit ball has sufficiently many extreme points, every 2-local nonlinear surjective isometry on a normed space is affine.