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AN INEQUALITY FOR DISTANCES AMONG FIVE POINTS AND DISTANCE PRESERVING MAPPINGS
- Authors
- Jung, Soon-Mo; Nam, Doyun
- Issue Date
- Dec-2018
- Publisher
- ELEMENT
- Keywords
- Inequalities; Aleksandrov-Rassias problem; distance; linear isometry; point
- Citation
- JOURNAL OF MATHEMATICAL INEQUALITIES, v.12, no.4, pp.1189 - 1199
- Journal Title
- JOURNAL OF MATHEMATICAL INEQUALITIES
- Volume
- 12
- Number
- 4
- Start Page
- 1189
- End Page
- 1199
- ISSN
- 1846-579X
- Abstract
- Using properties of norm and inner product, we prove a new inequality for distances between five points arbitrarily given in an inner product space. Moreover, we investigate the Aleksandrov-Rassias problem by proving that if the distance 1 is contractive and the golden ratio is extensive by a mapping f, then f is a linear isometry up to translation.
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