In 1940, the stability problem of functional equations was arose due to a question of Stanisław Ulam concerning the stability of group homomorphisms. Significant work was done by Donald H. Hyers about HYERS-ULAM STABILITY and obtained a partial affirmative answer to the question of Ulam in the context of Banach spaces in the case of additive mappings. In 1978, T. M. Rassias expanded Hyers's theorem for mappings between Banach spaces by considering an unbounded Cauchy difference subject to a continuity condition upon the mapping. After that many Researchers had studied about Hyers-Ulam stability of an additive quadratic type functional equations. In this research article , the Hyers-Ulam stability of an additive quadratic type functional equation was discussed and obtained the generalized Hyers-Ulam stability of additive quadratic type
functional equation f(x + ay) + af(x − y) = f(x − ay) + af(x + y) for any integer a with a ̸= −1, 0, 1 in 2-Banach space.