Mathematica Aeterna, Vol. 1, 2011, no. 04, 217 - 236 Generalized Ulam-Hyers stability of an AQ-functional equation in quasi-beta-normed spaces K.Ravi Department of Mathematics,Sacred Heart College Tirupattur - 635 601, TamilNadu, India shckravi@yahoo.co.in J.M.Rassias Pedagogical Department E.E,Section of Mathematics and Informatics National and Capodistrian University of Athens 4, Agamemnonos Str., Aghia Paraskevi,Athens 15342, Greece jrassias@primedu.uoa.gr,URL: http: www.primedu.uoa.gr/ jrassias R. Kodandan Department of Mathematics Sreeinivasa Institute of Technology and Management Studies Chittoor - 517 127, Andhra Pradesh, India,Rkodandan1979@rediffmail.com abstract In this paper, we introduce and investigate the general solution of a new func- tional equation f  x + y a + z + w b  + f  x + y a − z + w b  = 1 a 2 [(1 + a)f (x + y) + (1 − a)f (−x − y)] + 1 b 2 [f (z + w)+ f (−z − w)] where a, b ≥ 2 and discuss its Generalized Hyers - Ulam - Rassias stability in Quasi -β -normed spaces. Mathematics Subject Classification: [2000]: 39B52, 39B82,39B72,47Jxx. Keywords: Generalized Ulam-Hyers stability, Quadratic function, Additive function, Quasi-β -spaces, (β,p)-Banach spaces,Contractively subadditive, Ex- pansively super additive