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
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Keywords:
Additive Functional Equations, Quadratic Functional Equations, Mixed Type Functional Equations, Banach Space, Banach Algebra, Generalized Ulam-Hyers Stability, Fixed Point.Abstract
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 ô€€€ 2y; u ô€€€ 2v) = 4[g(x + y; u + v) + g(x ô€€€ y; u ô€€€ v)] ô€€€ 6g(x; u)
+ g(2y; 2v) + g(ô€€€2y;ô€€€2v) ô€€€ 4g(y; v) ô€€€ 4g(ô€€€y;ô€€€v)
Where  is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.
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