Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces
نویسندگان
چکیده
In this paper, using the direct method we study the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equations (2 ) ( ) 6 ( ) f x y f x y f x and (3 ) ( ) 16 ( ) f x y f x y f x for the mapping f from normed linear space in to 2-Banach spaces.
منابع مشابه
A Hyers-Ulam-Rassias stability result for functional equations in Intuitionistic Fuzzy Banach spaces
Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.
متن کاملGeneralized Hyers-Ulam Stability of Quadratic Functional Equations: A Fixed Point Approach
The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theorem was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has ...
متن کاملApproximate mixed additive and quadratic functional in 2-Banach spaces
In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.
متن کاملHyers-ulam-rassias Stability of the Apollonius Type Quadratic Mapping in Rn-spaces
Recently, in [5], Najati and Moradlou proved Hyers-Ulam-Rassias stability of the following quadratic mapping of Apollonius type Q(z − x) + Q(z − y) = 1 2 Q(x− y) + 2Q ( z − x + y 2 ) in non-Archimedean space. In this paper we establish Hyers-Ulam-Rassias stability of this functional equation in random normed spaces by direct method and fixed point method. The concept of Hyers-Ulam-Rassias stabi...
متن کاملApproximate a quadratic mapping in multi-Banach spaces, a fixed point approach
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}
متن کامل