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Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : be a bijective mapping with f(0) = 0 satisfying for all and, let be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N() such that lim N()=0 and a unique surjective isometry I : X Y satisfying for all .

GENERALIZED STABILITY OF ISOMETRIES ON REAL BANACH SPACES