General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized n-type additive-quadratic functional equation. g(x + 2y; u + 2v) + g(x ？？ 2y; u ？？ 2v) = 4[g(x + y; u + v) + g(x ？？ y; u ？？ v)] ？？ 6g(x; u) + g(2y; 2v) + g(？？2y;？？2v) ？？ 4g(y; v) ？？ 4g(？？y;？？v) Where is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.