Cone metric spaces and fixed point theorems in diametrically contractive mappings

Turkoglu D., Abuloha M.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, cilt.26, sa.3, ss.489-496, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 3
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10114-010-8019-5
  • Dergi Adı: ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.489-496
  • Anahtar Kelimeler: fixed point, cone metric space, diametrically contractive, sequentially compact, Lebesgue element, totally bounded, strongly minihedral
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets are compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.