Cone metric spaces and fixed point theorems in diametrically contractive mappings


Turkoglu D., Abuloha M.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, vol.26, no.3, pp.489-496, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1007/s10114-010-8019-5
  • Journal Name: ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.489-496
  • Keywords: fixed point, cone metric space, diametrically contractive, sequentially compact, Lebesgue element, totally bounded, strongly minihedral
  • Gazi University Affiliated: Yes

Abstract

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.