Abstract
In the first part of our paper we generalize the results obtained by Józef Tabor in [12] concerning the superstability of the Cauchy and Jensen functional equation almost everywhere.
In the second part we prove a general theorem on the superstablity of the Isometry equation in inner product spaces. As a corollary we determine when the Isometry Equation is superstable in the integral norm (this is a partial answer to [14]).
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J Tabor (1997) ArticleTitleStability of the Cauchy type equations in \( {\cal L}^{p} \) norms Results Math. 32 IssueID1-2 145–158 Occurrence Handle1464683 Occurrence Handle0890.39024 Occurrence Handle10.1007/BF03322534
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Tabor, J. Superstability of the Cauchy, Jensen and Isometry Equations. Results. Math. 35, 355–379 (1999). https://doi.org/10.1007/BF03322824
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DOI: https://doi.org/10.1007/BF03322824