Iterative Approximations Of Solutions For Nonlinear Variational Inclusions

In this paper, we study nonlinear variational inclusion problems in real reflexive Banach spaces. First, we briefly introduce the general situation of the research of nonli- near variational inclusion problems and the main work of this paper. Next, we study convergence problems of Ishikawa iterative sequences with mixed errors of solutions for a class of variational inclusion with φ-stongly accretive type mappings and establish a convergence theorem. Then, we study a class of variational inclusion problems with k- subaccretive type mappings. Convergence and stability theorems of the multi- step iterative sequences with errors of solutions for this class of variational inclusion problems are proved. More general convergence rate estimates are also given in our results. Finall, we introduce and study a class of variational inclusion problems with asymptotically φ-quasi-pseudocontractive type mappings. Strong convergence theorem of Ishikawa iterative sequences with random mixed errors of solutions for this class of variational inclusions is established without the conditions that sequence {t_n} or {s_n } is bounded. The results obtained in this paper improve and extend some known results.