The generalized Hyers–Ulam–Rassias stability of generalized derivations on unital normed algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

Abstract In this paper, we introduce a new integral transform, namely Aboodh and apply the transform to investigate Hyers–Ulam stability, Hyers–Ulam–Rassias Mittag-Leffler–Hyers–Ulam Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

Sometime in modeling applied problems there may be a degree of uncertainty in the parameters used in the model or some measurements may be imprecise. Due to such features, we are tempted to consider the study of functional equations in the fuzzy setting. The notion of fuzzy sets was first introduced by Zadeh [31] in 1965 which is a powerful hand set for modeling uncertainty and vagueness in var...

The generalized Hyers-Ulam-Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established. ∗2000 Mathematics Subject Classification. Primary 39B82; Secondary 46H25, 39B52, 47B47.

In this paper, the author established the general solution and generalized Ulam Hyers Rassias stability of n− dimensional Arun-additive functional equation f ( nx0 ± n ∑

‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept originated from Th. M. Rassias theorem that appeared his paper: On the linear mapping spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.