Approximately intertwining mappings

Let A be a Banach algebra, and let E be a weak Banach A-bimodule. An approximately intertwining mapping corresponding to a functional equation E(f ) = 0 is a mapping f :A→E with f (0) = 0 such that E(f ) ε, and for each a ∈ A the mappings fa(x) = f (ax) − af (x), af (x) = f (xa) −f (x)a, are continuous at a point. In this paper, we show that every approximately intertwining mapping corresponding to Cauchy, generalized Jensen or Trif functional equation can be estimated by an intertwining mapping. © 2006 Elsevier Inc. All rights reserved