Strong And Weak Convergence For Iterative Sequences Of Some Mappings

In this paper,we respectively study the strong and weak convergence for explicitand implicit iteration sequences of some mappings in Banach space.In Chapter 1, A sufficient and necessary condition is proved for Ishikawa itera-tive sequence of uniformly quasi-Lipschitzian mappings S,Twith errors to converge tofixed points, where S,T defined on a bounded convex set need not be continuous.In Chapter 2, We prove a sufficient and necessary condition for the implicit iter-ation sequence converges to a common fixed point of a finite family of asymptoticallyquasi-nonexpansive mappings in the intermediate sense in Banach spaces. We alsodiscuss the convergence of the implicit iteration sequence in uniformly convex Banachspaces.In Chapter 3, For the explicit iteration sequence constructed by a finite family ofnon-self asymptotically quasi-nonexpansive type,we obtain some conclusions of strongand weak convergence,respectively under some suitable conditions.