In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

Let X ,Y are linear space. In this paper, we prove the generalized Hyers-Ulam stability of the following quartic equation n ∑ k=2 ( k ∑ i1=2 k+1 ∑ i2=i1+1 . . . n ∑ in−k+1=in−k+1 ) f ( n ∑ i=1,i =i1,...,in−k+1 xi − n−k+1 ∑ r=1 xir )

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov's fixed point theorem and weakly Picard operator theory.

We will show the general solution of the functional equation f(x + ay) + f(x− ay) + 2(a − 1)f(x) = af(x + y) + af(x− y) + 2a(a − 1)f(y) and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.

In this paper, we will consider Hyers–Ulam–Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

The aim of this paper is to prove the stability in the sense of Hyers–Ulam stability of a polynomial equation. More precisely, if x is an approximate solution of the equation x + αx + β = 0, then there exists an exact solution of the equation near to x.

In this paper, we establish the general solution of the functional equation f(nx+ y) + f(nx− y) = nf(x+ y) + nf(x− y) + 2(f(nx)− nf(x))− 2(n − 1)f(y) for fixed integers n with n 6= 0,±1 and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

The stability of the functional equation f(x composite function y) = H(f(x), f(y)) (x, y in S) is investigated, where H is a homogeneous function and composite function is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Abstract In this paper, we investigate the existence and uniqueness of a solution for class ψ -Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, Krasnosellskii’s fixed point theorems. Further, applying techniques nonlinear functional analysis, establish various kinds Ulam stability results analyzed problem,...