[en] Let E be a real q-uniformly smooth Banach space. Suppose T is a set-valued locally strongly accretive map with open domain D(T) in E and that 0 is an element of Tx has a solution x* in D(T). Then there exists a neighbourhood B in D(T) of x* and a real number r₁>0 such that for any r>r₁ and some real sequence {c_n}, any initial guess x₁ is an element of B and any single-valued selection T₀ of T, the sequence {x_n} generated from x₁ by x_n+1=x_n-c_nT₀x_n, n≥1, remains in D(T) and converges strongly to x* with ||x_n-x*|| O(n^-(q-1)/q). A related result deals with iterative approximation of a solution of the equation f is an element of x+Ax when A is a locally accretive map. Our theorems generalize important known results and resolve a problem of interest. (author). 39 refs