Approximating fixed points of non-self asymptotically nonexpansivemappingsin Banach spaces

[摘要] SupposeKis a nonempty closed convex nonexpansive retract of areal uniformly convex Banach spaceEwithPas a nonexpansiveretraction. LetT:K→Ebe an asymptoticallynonexpansive mapping with{kn}⊂[1,∞)such that∑n=1∞(kn−1)<∞andF(T)is nonempty, whereF(T)denotes the fixed points set ofT. Let{αn},{αn'}, and{αn''}be real sequences in (0,1) andε≤αn,αn',αn''≤1−εfor alln∈ℕand someε>0. Starting from arbitraryx1∈K, define the sequence{xn}byx1∈K,zn=P(αn''T(PT)n−1xn+(1−αn'')xn),yn=P(αn'T(PT)n−1zn+(1−αn')xn),xn+1=P(αnT(PT)n−1yn+(1−αn)xn). (i) If the dualE*ofEhas theKadec-Kleeproperty, then{xn}convergesweakly to a fixed pointp∈F(T); (ii) ifTsatisfies condition (A), then{xn}converges strongly to a fixed pointp∈F(T).

[学科分类] 应用数学