A generalization of some well-known distances and related isometries

Colakoglu H. B., Kaya R.

MATHEMATICAL COMMUNICATIONS, vol.16, no.1, pp.21-35, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 1
  • Publication Date: 2011
  • Journal Name: MATHEMATICAL COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.21-35
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this paper, we define a family of distance functions in the real plane, m-distance function, which includes the taxicab, Chinese checker, maximum, and alpha distance 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 isometrics 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.