we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy version. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

We prove a general result on Ulam's type stability of the functional equation f(x + y) = f(x) + f(y), in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.

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 equ...

and Applied Analysis 3 Moreover, they also investigated the Hyers-Ulam-Rassias stability of 1.3 by using the direct method see 18 . Indeed, they tried to approximate the even and odd parts of each solution of a perturbed inequality by the even and odd parts of an “exact” solution of 1.3 , respectively. In Theorems 3.1 and 3.3 of this paper, we will apply the fixed point method and prove the Hye...

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...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.