A fixed point approach to the stability of the n-dimensional quadratic and additive functional equation

Abstract

In this paper, we investigate the stability of the functional equation f ⎛ ⎝ n j=1 x j ⎞ ⎠ + (n − 2) n j=1 f (x j) − 1≤i<j≤n f (x i + x j) = 0 by using the fixed point theory in the sense of L. Cȃdariu and V. Radu.

A fixed point approach to the stability of a mixed type additive and quadratic functional equation

“…Indeed, he applied the fixed point method to prove the stability of Cauchy functional equations, Jensen's functional equations, and quadratic functional equations (see [2,3,4,5]). After his work, many authors used the fixed point method to prove the stability of various functional equations [13,14,15,16,17,18,19,20].…”

On the Generalized Hyers-Ulam Stability of ann-Dimensional Quadratic and Additive Type Functional Equation

“…. , ∈ ( > 2) (see also [11][12][13][14][15]). The functional equation (2) is a quadratic-additive type functional equation (see Theorem 2.6 in [16]).…”

On the stability of the n-dimensional quadratic and additive functional equation in random normed spaces via fixed point method

“…In 2006, K.-W. Jun and H.-M. Kim [9] investigated the stability of the functional equation (2) in classical normed spaces by using the direct method. Recently, the authors proved the stability of the functional equation (2) in fuzzy spaces [8] and used the fixed point method [7] to prove the stability for the functional equation (2) in Banach spaces. It is easy to see that the mappings f (x) = ax 2 + bx is a solution of the functional equation (2).…”