Acta mathematica scientia,Series B ›› 1989, Vol. 9 ›› Issue (4): 463-477.
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Huang Senzhong
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Abstract: By considering the connection of approximate isometry with isometry we study the following problem "For what subclass of (F)-normed spaces the metric structure completely determines the linear constructure and further, what form can be taken when we represent an approximate isometry as a perturbation of isometry. We introduce a subclass of so-called midpoint p-constracted (F)-normed spaces. For this subclass some new results are obtained and especially the known results of Mazur-Ulam and Gervitz-Gruber are extended.
Huang Senzhong. APPROXIMATE ISOMETRIES ON (F)-NORMED SPACES[J].Acta mathematica scientia,Series B, 1989, 9(4): 463-477.
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