A generalization of some well-known distances and related isometries
MATHEMATICAL COMMUNICATIONS, cilt.16, sa.1, ss.21-35, 2011 (SCI-Expanded, Scopus)
- 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.