Iterative Scheme with Errors for Common Zeros of Finite Accretive Mappings and Nonlinear Elliptic Systems

Abstract

We present a new iterative scheme with errors to solve the problems of finding common zeros of finite $m$-accretive mappings in a real Banach space. Strong convergence theorems are established, which extend the corresponding works given by some authors. Moreover, the relationship between zeros of $m$-accretive mappings and one kind of nonlinear elliptic systems is investigated, from which we can see that some restrictions imposed on the iterative scheme are valid and the solution of one kind of nonlinear elliptic systems can be approximated by a suitably defined iterative sequence.