International Journal of Applied Science and Mathematical Theory ISSN 2489-009X Vol. 2 No.3 2016 www.iiardpub.org IIARD – International Institute of Academic Research and Development Page 53 On reducible and Like – Generalized Recurrent Space Fahmi Yaseen Abdo Qasem & Ala'a Abdalnasser Awad Abdallah Dept. of Math., Faculty of Education-Aden, Univ. of Aden, Khormakssar, Aden, Yemen fahmi.yaseen@yahoo.com, ala733.ala00@Gmail.com Abstract In this paper, we introduced the generalized recurrent Finsler space, i.e. characterized by the following condition ( ) , , Where is Berwald's covariant differential operator with respect to , and are known as recurrence vectors . The purpose of the present paper to develop the above space by study the properties of a reducible space and a - like space, which their called a reducible ge neralized recurrent space and a – like generalized recurrent space, respectively. Also to obtain different theorems for some tensors satisfy in above spaces. Various identities are established in our spaces. Keywords: a reducible generalized recurrent space and a – like generalized recurrent space. 1. Introduction R. Verma [7] obtained the condition of a reducible recurrent space be a necessarily a Landsberg space. In Rund's book, defined here, is defined by . This difference must be noted. M. Matsumoto [5] showed that the curvature tensor of a three dimensional Finsler space satisfies the condition and called it like Finsler space. Some properties of a like Finsler space were studied by H. Izumi and T.N. Srivastava [3] by introducing the idea of indicatorization. M. Yoshida [6] also discussed a like Finsler space and its special cases. Let be an n – dimensional Finsler space equipped with the metric function F(x,y) satisfying the request conditions [2] . The vector is defined by (1.1) ( ) The two sets of quantities and its associative , which are components of a metric tensor connected by (1.2) { In view of (1.1) and (1.2), we have (1.3) a) , b) and c) . The tensor is defined by