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In this paper, we investigate the stability of an additive-quadratic-quartic functional equation

We have proved theHyers-Ulam stability and the hyperstability of the quadratic functional equation f (x + y + z) + f (x + y − z) + f (x − y + z) + f (−x + y + z) = 4[f (x) + f (y) + f (z)] in the class of functions from an abelian group G into a Banach space.

In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. [ABSTRACT FROM AUTHOR]

We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space. [ABSTRACT FROM AUTHOR]

We establish some stability results over p-adic fields for the generalized quadratic functional equation ...where n ? N and n = 2. [ABSTRACT FROM AUTHOR]

Let X be a normed space and Y a sequentially complete Hausdorff topological vector space over the field Q of rational numbers. Let D1 = {(x, y) ∈ X x X : ||x|| + ||y|| ≥ d}, and D2 = {(x, y) ∈ X x X : ||x|| + ||y|| < d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on D1(D2), and taking values in Y. We consider also the Pexiderized Cauchy functional equation. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we prove that approximate trigonometric functions are bounded. That is, if a non-zero function satisfies the inequality or , then is bounded. [Copyright &y& Elsevier]

In this paper, we investigate the generalized Hyers–Ulam stability for the generalized psi functional equation f (x + p) = f (x) + φ (x) by the direct method in the sense of P. Gǎvruta and the Hyers–Ulam–Rassias stability. [ABSTRACT FROM AUTHOR]

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f (x 1 + y 1 , x 2 + y 2 , ... , x n + y n) = f (x 1 , x 2 , ... , x n) + f (y 1 , y 2 , ... , y n). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the generalized Hyers-Ulam stability of the Pexider functional equation f (x + y , z + w) = g (x , z) + h (y , w) . [ABSTRACT FROM AUTHOR]