Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .

In this paper, we investigate the generalized Hyers–Ulam stability for the functional equation f(ax+y)+af(y−x)− a(a+ 1) 2 f(x)− a(a+ 1) 2 f(−x)− (a+1)f(y) = 0 in non-Archimedean normed spaces. Mathematics Subject Classification: 39B52, 39B82

A familiar functional equation f(ax+b) = cf(x) will be solved in the class of functions f : R → R. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f ( a1x1+···+amxm+x0 )= m ∑ i=1 bif ( ai1x1+···+aimxm ) in connection with the question of Rassias and Tabor.

We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f(x + y) + f(x − y) = 2f(x) + 2f(y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove a generalized version of fuzzy stability o...

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains. 1. Introduction. The starting point of studying the stability of functional equations seems to be the famous talk of Ulam ...

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f(x+y+z)+f(x−y)+f(x−z) = f(x−y−z)+f(x+y)+f(x+z) is what is taken into account to be dealt with in this paper.

In this paper, we introduced the notion of a generalized multivalued (α,φ)-almost contractions and establish the existence of fixed point theorems for this class of mapping. The results presented in this paper generalize and extend some recent results in multivalued almost contraction. Also, we show its applications in the Ulam-Hyers stability of fixed point problems for multivalued operators.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation 3(f(x+ 2y) + f(x− 2y)) = 12(f(x + y) + f(x− y)) + 4f(3y)− 18f(2y) + 36f(y)− 18f(x).

In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x− 2y) = 4f(x + y) + 4f(x− y)− 6f(x) + f(2y) + f(−2y)− 4f(y)− 4f(−y) in non-Archimedean Banach spaces.

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for quadratic functional equations f(2x+ y)+ f(2x− y) = f(x+ y)+ f(x− y)+6f(x) and f(2x + y) + f(x + 2y) = 4f(x + y) + f(x) + f(y).