Solution and Stability of n-Dimensional Quadratic Functional Equation

Solution and intuitionistic fuzzy stability of n- dimensional quadratic functional equation: direct and fixed point methods

“…, x n ∈ X. Hence Q satisfies the quadratic functional equation (4). In order to prove Q(x) is unique, we let Q (x) be another quadratic functional equation satisfying (4) and (16).…”

“…for all r > 0 and all x 1 , x 2 , · · · , x n ∈ X By proceeding the same procedure as in the Theorem 4.1, we can prove the function, Q : X → Y satisfies the functional equation (4). By fixed point alternative, since Q is unique fixed point of T in the set…”

“…The mapping f : X → Y satisfies the functional equation (1) for all x, y ∈ X if and only if f : X → Y satisfies the functional equation (4) for all x 1 , · · · , x n ∈ X .…”

“…Let f : X → Y satisfies the functional equation (4). Replacing (x 2 , x 3 , · · · , x n ) by (0, 0, · · · , 0) in (4), we get…”

Perturbation of n dimensional AQ - mixed type functional equation via Banach spaces and Banach algebra : Hyers direct and alternative fixed point methods

“…Chang et al, [6]. Recently, M. Arunkumar and S. Karthikeyan [3] introduced and established the general solution and generalized Ulam-Hyers stability of n−dimensional mixed type additive and quadratic functional equation of the form…”