A Generalization of The Taxicab Metric And Related Isometries

Authors : Harun Barış Çolakoğlu

Pages : 158-162

View : 14 | Download : 5

Publication Date : 2018-04-15

Article Type : Research

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