Summary: Let be a uniformly smooth real Banach space and let be a mapping with . Suppose that is a generalized Lipschitz generalized -quasi-accretive mapping. Let and be real sequences in [0,1] satisfying the following conditions: (i) ; (ii) ; (iii) ; (iv) Let be generated iteratively from arbitrary by
where is defined by forall and is an arbitrary bounded sequence in . Then there exists such that if the sequence converges strongly to the unique solution of the equation . A related result deals with approximation of the unique fixed point of a generalized Lipschitz and generalized -hemi-contractive mapping.