Stability of generalized Cauchy equations

Stability of Generalized Additive Cauchy Equations

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.

Generalized Cauchy Difference Equations. Ii

The main result is an improvement of previous results on the equation f(x) + f(y)− f(x+ y) = g[φ(x) + φ(y)− φ(x+ y)] for a given function φ. We find its general solution assuming only continuous differentiability and local nonlinearity of φ. We also provide new results about the more general equation f(x) + f(y)− f(x+ y) = g(H(x, y)) for a given function H. Previous uniqueness results required ...

Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

On Generalized Cauchy and Pexider Functional Equations over a Field

Let lK be a commutative field and (P, +) be a uniquely 2-divisible group (not necessarily abelian). We characterize all functions T: IK -+ P such that the Cauchy difference T(s+ t) T(t) T(s) depends only on the product st for all s, t E ~{. Further, we apply this result to describe solutions of the functional equation F(s + t) = K(st) 0 H(s) 0 G(t), where the unknown functions F, K, H, G map th...