Iterative construction of fixed points of nonself-mappings in Banach spaces

The purpose of this paper is to study the iterative methods for constructing fixed points of nonself-mappings in Banach spaces. The concept of the class of asymptotically QGQG-weakly contractive nonself-mappings is introduced and a new iterative algorithm for finding fixed points of this class of mappings is studied. Several strong convergence results on this algorithm are established under different conditions.