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- W86347829 abstract "In this paper, we deflne a family of distance functions in the real plane, m- distance function, which includes the taxicab, Chinese checker, maximum, and alpha dis- tance functions as special cases, and we show that the m-distance function determines a metric. Then we give some properties of the m-distance, and determine isometries of the plane with respect to the m-distance. Finally, we extend the m-distance function to three- and n-dimensional spaces, and show that each extended distance function determines a metric. We also give some properties of the m-distance in three-dimensional space. AMS subject classiflcations: 51K05, 51K99, 51F99, 51N99" @default.
- W86347829 created "2016-06-24" @default.
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- W86347829 date "2011-06-10" @default.
- W86347829 modified "2023-09-24" @default.
- W86347829 title "A generalization of some well-known distances and related isometries" @default.
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