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

Authors : Thabet ABDELJAWAD

Pages : 235-240

View : 15 | Download : 8

Publication Date : 2011-04-05

Article Type : Other Papers

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 insert ignore into journalissuearticles values(5);:2259-2261 insert ignore into journalissuearticles values(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