Picard-like iterations for nonlinear equations involving <inline-formula><graphic file="1029-242X-2002-703904-i1.gif"/></inline-formula>-accretive operators

Let be an arbitrary real normed linear space and let be a -Lipschitz strongly -accretive operator. It is proved that Picard-like iteration processes converge strongly to the unique solutions of the operator equations and where is an arbitrary but fixed vector. Related results deal with the strong convergence of Picard-like iteration processes to the unique solution of equations involving linear -positive definite ( -p.d) operators. Nontrivial examples, indicating that this class of mappings properly contains the classes of nonlinear accretive, dissipative and linear -p.d. operators, are also given.