Fixed Points and Fuzzy Stability of Functional Equations Related to Inner Product

Abstract

In [40], Th.M. Rassias introduced the following equality, then the mapping f : V → W is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equationwhich is called a quadratic functional equation. Every solution of the quadratic functional equation is said to be a quadratic mapping.Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

Generalized Hyers-Ulam Stability of Quadratic Functional Inequality

“…, ∈ with ∑ =1 = 0, then the mapping is realized as the sum of an additive mapping and a quadratic mapping [25]. Park [25] and Jang et al [26] have proved the generalized Hyers-Ulam stability of the functional equation (7). In particular, if = 3 and even function satisfies (7), then it is easy to see that satisfies the equation…”

Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications

“…Gȃvruta [7] generalized the Rassias' result. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [5,6], [9,10], [12]- [19], [21]- [23], [28]- [30]). …”