Completion of TVS-Cone Metric Spaces and Some Fixed Point Theorems

Year 2011, Volume: 24 Issue: 2, 235 - 240, 05.04.2011

Thabet Abdeljawad

Abstract

In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed space over a complete locally convex topological vector space E are proved. The completion spaces are de- fined by means of an equivalence relation obtained by convergence via the topology of the locally convex space E. Very recently some fixed point theorems obtained in cone Banach spaces are generalized to locally convex cone Banach spaces. These theorems can not be generalized or proved trivially by using  the  nonlinear scalarization function used very recently by Wei-Shih Du in ” A note on cone  metric  fixed point  theory and its equivalence, Nonlinear Analysis  Theory Methods and Applications 72 (5):2259-2261 (2010)”.

Key Words: Cone metric space, tvs- cone metric.space, tvs- cone Banach space, fixed point, normal cone.

Keywords

Cone metric space, tvs- cone metric.space, tvs- cone Banach space, fixed point, normal cone.

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