Convergence and stability of some iterative processes for a class of quasinonexpansive type mappings

Motivated by Dotson s example we consider a certain class of mappings which includes the classes of mappings studied by Zamfirescu, Ćirić, Berinde and others. We prove several new results about convergence of distinct iterative processes in convex metric spaces. Furthermore, we study the stability for this class of mappings in the setting of metric spaces.