Mathematica Aeterna, Vol. 1, 2011, no. 06, 353 - 359 T- Reich Mapping in Topological Vector Space-Valued Cone Metric Spaces S. K. Malhotra Dept. of Mathematics, Govt. S.G.S.P.G. College Ganj Basoda, Vidisha (M.P.) India S. Shukla Dept. of Applied Mathematics, S.V.I.T.S Sanwer Road, Indore (M.P.) India satishmathematics@yahoo.co.in R. Sen Dept. of Applied Mathematics, S.V.I.T.S Sanwer Road, Indore (M.P.) India ravindra sen13@yahoo.co.in Abstract The object of this paper is to establish some new fixed point results in topological vector space-valued cone metric spaces, by proving the fixed point theorems for T-Reich and T-Kannan contraction mappings in topological vector space-valued cone metric spaces. Mathematics Subject Classification: 54H25, 47H10. Keywords: TVS-Cone Metric Space, Fixed Point, Contraction Mapping. 1 Introduction Huang and Zhang [5] generalized the notion of metric spaces replacing the set of real numbers by an ordered Banach space. Many authors proved fixed point theorems in cone metric spaces (see, e.g. [5, 6, 12] ) under additional assumption about the underlying cone, such as normality or even regularity. Recently, Rezapour and Hamlbarani [11] omitted the assumption of normality in cone metric space, which is a milestone in developing fixed point theory in