On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation inn-Banach Spaces

On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n-Banach Spaces

and Applied Analysis 3 Definition 1.4. A sequence {xk} in an n-normed space X is said to converge to some x ∈ X in the n-norm if lim k→∞ ∥ ∥xk − x, y2, . . . , yn ∥ ∥ 0, 1.4 for every y2, . . . , yn ∈ X. Definition 1.5. A sequence {xk} in an n-normed space X is said to be a Cauchy sequence with respect to the n-norm if lim k,l→∞ ∥ ∥xk − xl, y2, . . . , yn ∥ ∥ 0, 1.5 for every y2, . . . , yn ∈ X...

Hyers-Ulam Stability of Fibonacci Functional Equation

On the Stability of a General Mixed Additive-Cubic Functional Equation in Random Normed Spaces

1 Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China 2 Pedagogical Department E.E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, 4, Agamemnonos Str., Aghia Paraskevi, 15342 Athens, Greece 3 School of Communication and Information Engineering, University of Electronic Science and Technology of China, Che...

Hyers-Ulam-Rassias stability of a composite functional equation in various normed spaces

In this paper, we prove the generalized Hyers-Ulam(or Hyers-Ulam-Rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

and Applied Analysis 3 with f 0 0 in a non-Archimedean space. It is easy to see that the function f x ax bx2 is a solution of the functional equation 1.8 , which explains why it is called additive-quadratic functional equation. For more detailed definitions of mixed type functional equations, we can refer to 26–47 . Definition 1.1 see 48 . Let X be a real vector space. A function N : X × R → 0,...