quadratic $alpha$-functional equations
نویسندگان
چکیده
in this paper, we solve the quadratic $alpha$ -functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f( alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.
منابع مشابه
Quadratic $alpha$-functional equations
In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.
متن کاملFuzzy Stability of Quadratic Functional Equations
Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...
متن کاملQuadratic-Quartic Functional Equations in RN-Spaces
The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms. Let G1, · be a group and let G2, ∗, d be a metric group with the metric d ·, · . Given > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h x · y , h x ∗ h y < δ for all x, y ∈ G1, then there exists a homomorphism H...
متن کاملQuadratic Functional Equations of Pexider Type
First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.
متن کاملFuzzy Stability of Additive–quadratic Functional Equations
In this paper we investigate the generalized HyersUlam stability of the functional equation f(2x + y) + f(2x − y) = f(x + y) + f(x − y) + 2f(2x)− 2f(x) in fuzzy Banach spaces.
متن کاملA fixed point approach to the stability of additive-quadratic-quartic functional equations
In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
international journal of nonlinear analysis and applicationsجلد ۸، شماره ۱، صفحات ۱-۹
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023