A Generalization of The Taxicab Metric And Related Isometries

Year 2018, Volume: 6 Issue: 1, 158 - 162, 15.04.2018

Harun Barış Çolakoğlu

Abstract

In this paper, we define a family of distance functions in the real plane, \textit{m}-generalized taxicab distance function, which includes the generalized taxicab distance and so the taxicab distance functions as special cases, and we show that the \textit{m}-generalized taxicab distance function determines a metric. Then we give some properties of the \textit{m}-generalized taxicab metric, and determine Euclidean isometries that preserve the \textit{m}-generalized taxicab metric.

Keywords

metric, taxicab distance, generalized taxicab distance, isometry

References

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