International Journal of Pure and Applied Mathematics Volume 96 No. 3 2014, 299-306 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v96i3.1 P A ijpam.eu ON THE MAZUR-ULAM THEOREM IN FUZZY ANTI-2-NORMED SPACES Majid Abrishami-Moghaddam Department of Mathematics Birjand Branch Islamic Azad University Birjand, IRAN Abstract: In this article, we study the notions of 2-isometries in fuzzy anti-2- normed spaces and prove a Mazur-Ulam type theorem in the 2-strictly convex fuzzy anti-2-normed spaces. AMS Subject Classification: 46S40, 39B52, 39B82, 26E50, 46S50 Key Words: fuzzy anti-2-normed space, Mazur-Ulam theorem, 2-strictly convex, 2-collinear 1. Introduction The theory of fuzzy sets was introduced by L. Zadeh [14] in 1965 and thereafter several authors applied it different branches of pure and applied mathematics. Many mathematicians considered the fuzzy normed spaces in several angels (see [3], [10], [13]). In [8] Iqbal H. Jebril and Samanta introduced fuzzy anti-norm on a linear space depending on the idea of fuzzy anti-norm was introduced by Bag and Samanta [1] and investigated their important properties. Let X and Y be metric spaces with metrics d X and d Y , respectively. A map f : X → Y is called an isometry if d Y (f (x),f (y)) = d X (x, y) for every x, y ∈ X. In 1932, the theory of isometric mappings was originated in the classical paper Received: January 25, 2014 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu