- Gazi University Journal of Science
- Vol: 24 Issue: 2
- Completion of TVS-Cone Metric Spaces and Some Fixed Point Theorems
Completion of TVS-Cone Metric Spaces and Some Fixed Point Theorems
Authors : Thabet Abdeljawad
Pages : 235-240
View : 8 | Download : 3
Publication Date : 2011-04-05
Article Type : Other
Abstract :In this pa p er a completion theorem for cone metric spaces and a completion theorem for cone normed space ov er a complete l o cally co nv ex to p ological v ector space E are pr ov ed. The completion spaces are de- fined b y means of an equi v al ence relation obtained b y co nv ergence via the to p ology of the l o cally co nv ex space E . V ery rece n tly some fixed p oi n t theorems obtained in cone Bana c h spaces are generalized to l o cally co n v ex cone Bana c h spaces. These theorems can not b e generali z ed or pr ov ed trivially b y using the nonlinear scalarization function used v ery rece n tly b y W ei-Shih Du in ” A note on cone metric fixed p oi n t theory and its equi v alence, Nonlinear Analysis Theory Meth o ds and Applications 72 (5):2259-2261 (2010)”. Key W ords : C one metric space, tvs- cone metric. space, tvs- cone Bana c h space, fixed p oi n t, normal cone.Keywords : Cone metric space, tvs- cone metric.space, tvs- cone Banach space, fixed point, normal cone.