A generalization of some well-known distances and related isometries

ÇOLAKOĞLU H. B., Kaya R.

MATHEMATICAL COMMUNICATIONS, cilt.16, sa.1, ss.21-35, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2011
  • Dergi Adı: MATHEMATICAL COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.21-35
  • Anahtar Kelimeler: metric, m-distance, taxicab distance, Chinese checker distance, maximum distance, alpha distance, minimum distance set, isometry
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.