Some Generalizations of Ulam-Hyers Stability Functional Equations to Riesz Algebras

Abstract EN

Badora (2002) proved the following stability result.

Let ε and δ be nonnegative real numbers, then for every mapping f of a ring R onto a Banach algebra B satisfying ||f(x+y)-f(x)-f(y)||≤ε and ||f(x⋅y)-f(x)f(y)||≤δ for all x,y∈R, there exists a unique ring homomorphism h:R→B such that ||f(x)-h(x)||≤ε, x∈R.

Moreover, b⋅(f(x)-h(x))=0, (f(x)-h(x))⋅b=0, for all x∈R and all b from the algebra generated by h(R).

In this paper, we generalize Badora's stability result above on ring homomorphisms for Riesz algebras with extended norms.