A New Generalization of a Theorem of Jung for the Orthogonality Equation

The main result of this paper states as follows: Assume that for a closed ball D @ 0 and with center at the origin, a mapping T : D M D satisfies $$ T(0) = 0\ \hbox{and}\ \vert \langle Tx, Ty \rangle - \langle x, y \rangle \vert \leq \varepsilon \eqno (1) $$ for some 0 h l < min { 1/4, d 2 /17} and for all x , y ] D . Then, there exists an isometry I : D M D with $$ \vert Tx - Ix \vert \le \left\{ {\matrix{ {13\sqrt \varepsilon } \hfill &{{\rm for}\; d

Keywords:

• Hyers-Ulam Stability
• Isometry
• Orthogonality Equation
• Inner Product Space