The Convergence Theorems Of Iteration Sequence Of ?-Nonexpasive Mappings

In this thesis,the demiclosed principle of monotone ?-nonexpansive map-ping is showed in a uniformly convex Banach space with the partial order "?".With the help of such a demiclosed principle,the strong convergence of Mann iter-ation of monotone ?-nonexpansive mapping T are proved without some compact conditions such as semi-compactness of T?and the weakly convergent conclusions of such an iteration are studied without the conditions such as Opial's condition.These convergent theorems are obtained under the iterative coefficient satisfying the condition,?k=1 +?min {?k,(1-?k)}=+?,which contains ?k=1/k+1 as a special case.The Halpern-Mann iteration in introduced for an ?-nonexpansive mapping as follow,x n+1=?nu +(1-?n)(?nTxn+(1-?)xn),such type of mappings contains classical nonexpansive mapping and ?-hybrid mapping as special cases.The strong convergence theorems of such an iteration sequence to a fixed point PF(T)u of an are showed ?-nonexpansive mapping,and the fixed point is a metric projection point of the point u to the fixed point set of such a mapping.