M. Eshaghi Gordji

Approximate ternary Jordan derivations on Banach ternary algebras

Let A be a Banach ternary algebra over a scalar field R or C and X be a ternary Banach A-module. A linear mapping D:(A,[ ]A)→(X,[ ]X) is called a ternary Jordan derivation if D([xxx]A)=[D(x)xx]X+[xD(x)x]X+[xxD(x)]X for all x∊A. In this paper, we investigate ternary Jordan derivations on Banach ternary algebras, associated with the following functional equation f((x+y+z)/4)+f((3x−y−4z)/4)+f((4x+3z)/4)=2f(x). Moreover, we prove the generalized Ulam–Hyers stability of ternary Jordan derivations on Banach ternary algebras.

Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces

We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation in quasi-Banach spaces.

Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces

Abstract In this paper, we prove the Hyers–Ulam–Rassias stability of the mixed type cubic–quartic functional equation f ( x + 2 y ) + f ( x − 2 y ) = 4 ( f ( x + y ) + f ( x − y ) ) − 24 f ( y ) − 6 f ( x ) + 3 f ( 2 y ) in non-Archimedean normed spaces.

On the stability of J∗-derivations

In this paper, we establish the stability and superstability of J∗-derivations in J∗-algebras for the generalized Jensen–type functional equation rf(x+yr)+rf(x−yr)=2f(x). Finally, we investigate the stability of J∗-derivations by using the fixed point alternative.

N-JORDAN HOMOMORPHISMS

Let n ∈ℕ and let A and B be rings. An additive map h : A → B is called an n -Jordan homomorphism if h ( a n )=( h ( a )) n for all a ∈ A . Every Jordan homomorphism is an n -Jordan homomorphism, for all n ≥2, but the converse is false in general. In this paper we investigate the n -Jordan homomorphisms on Banach algebras. Some results related to continuity are given as well.

On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations where are nonzero fixed integers with , and for fixed integers with and .

STABILITY OF MIXED TYPE CUBIC AND QUARTIC FUNCTIONAL EQUATIONS IN RANDOM NORMED SPACES

We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary -norms .

On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces

We establish the general solution of the functional equation for fixed integers with and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C∗-ternary algebras

Let A be a C∗-ternary algebra. A C-bilinear T:A×A→A is called a C∗-ternary algebra bi-multiplier, if it satisfies T([abc],d)=[T(a,b)cd], T(a,[bcd])=[abT(c,d)] for all a,b,c,d∊A. Also, the mapping T:A×A→A is a called C∗-ternary algebra Jordan bimultiplier, if it satisfies T([aaa],a)=[T(a,a)aa], T(a,[aaa])=[aaT(a,a)] for all a∊A. Using the fixed point method, we investigate the generalized Hyers–Ulam–Rassias stability of bimultipliers and Jordan bimultipliers in C∗-ternary algebras. The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in his paper: [Th. M. Rassias, Proc. Am. Math. Soc. 72, 297 (1978)].

Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation

We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation .