International Journal of Pure and Applied Mathematics Volume 86 No. 6 2013, 951-963 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v86i6.8 P A ijpam.eu ADDITIVE QUADRATIC FUNCTIONAL EQUATION ARE STABLE IN BANACH SPACE: A FIXED POINT APPROACH M. Arunkumar 1 , P. Agilan 2 1 Department of Mathematics Government Arts College Tiruvannamalai, 606 603, TamilNadu, INDIA Department of Mathematics S.K.P. Engineering College Tiruvannamalai, 606 611, TamilNadu, INDIA Abstract: In this paper, the authors established the generalized Ulam - Hyers stability of a mixed type Additive Quadratic(AQ)-functional equation f (x +2y +3z)+ f (x − 2y +3z)+ f (x +2y − 3z)+ f (x − 2y − 3z) =4f (x) + 8[f (y)+ f (−y)] + 18[f (z)+ f (−z)] in Banach spaces using fixed point approach. AMS Subject Classification: 39B52, 32B72, 32B82 Key Words: additive functional equations, quadratic functional equation, mixed type functional equation, Ulam-Hyers stability, fixed point 1. Introduction S.M. Ulam [25] is the pioneer for the famous stability problem in functional equations. In 1940, while he was delivering a talk before the Mathematics Club of University of Wisconsin, he proposed a number of unsolved problems. Among those was the following question concerning the stability of homomorphisms: Received: May 9, 2013 c  2013 Academic Publications, Ltd. url: www.acadpubl.eu