Abstract
In this paper, we consider 2-isometries, 2-continuous mappings and mappings preserving equality of 2-distance and investigate the relation between the three mappings in linear 2-normed spaces. We prove that if f: E → F is a mapping preserving equality of 2-distance with its gauge function injective, f is 2-continuous and the range of f contains a segment, then f is affine. Moreover, when dimensionE < 2, the condition that f is 2-continuous could be eliminated. *This work was supported by the National Natural Science Foundation of China, Grant No. 10871101.
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