Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem


ABDELJAWAD T., Turkoglu D.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, cilt.14, sa.3, ss.484-494, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 14 Konu: 3
  • Basım Tarihi: 2012
  • Dergi Adı: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.484-494

Özet

Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used recently by Wei-Shih Du in [A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove the equivalence of the Banach contraction principle in cone metric spaces and usual metric spaces. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.