Let X be a real Banach space with a uniformly convex dual, X*, and let C be a nonempty closed convex and bounded subset of X. Let T: C → C be a strongly accretive and a continuous mapping. For any f ∈ C, let S: C → C be defined by Sx = f + x – Tx for each x ∈ C. Then, the iteration process xo ∈ C,
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0004972700012077/resource/name/S0004972700012077_eqnU1.gif?pub-status=live)
under suitable conditions on the real sequence
converges strongly to a solution of the equation Tx = f in C. Furthermore, if T is strongly accretive and Lipschitz with Lipschitz constant L ≥ 1 then the iteration process x0 ∈ C,
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0004972700012077/resource/name/S0004972700012077_eqnU2.gif?pub-status=live)
under suitable conditions on the real sequences
and
converges strongly to a solution of the equation Tx = f in C. Explicit error estimates are obtained.