On generalized taxicab metric in three dimensional space

Abstract

In this paper, we define the generalized taxicab distance function in three dimensional space, which includes the taxicab distance function as a special case, and we show that three dimensional generalized taxicab distance function determines a metric. Then we give some properties of three dimensional generalized taxicab metric, and determine Euclidean isometries of the space preserving the generalized taxicab metric.