Stability of a Quartic and Orthogonally Quartic Functional Equation
نویسنده
چکیده
In this paper, the authors investigate the generalized Hyers-UlamAoki-Rassias stability of a quartic functional equation g(2x+ y + z) + g(2x+ y − z) + g(2x− y + z) + g(−2x+ y + z) + 16g(y) + 16g(z) = 8[g(x+ y) + g(x− y) + g(x+ z) + g(x− z)] + 2[g(y + z) + g(y − z)] + 32g(x). (1) The above equation (1) is modified and its Hyers-Ulam-Aoki-Rassias stability for the following quartic functional equation f(2x+ y + z) + f(2x+ y − z) + f(2x− y + z) + f(−2x+ y + z) + f(2y) + f(2z) = 8[f(x+ y) + f(x− y) + f(x+ z) + f(x− z)] + 2[f(y + z) + f(y − z)] + 32f(x) (2) for all x, y, z ∈ X with x ⊥ y, y ⊥ z and z ⊥ x is discussed in orthogonality space in the sense of Rätz.
منابع مشابه
Intuitionistic fuzzy stability of a quadratic and quartic functional equation
In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.
متن کاملCubic-quartic functional equations in fuzzy normed spaces
In this paper, we investigate the generalizedHyers--Ulam stability of the functional equation
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 کاملStability of generalized QCA-functional equation in P-Banach spaces
In this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.
متن کامل