Banach空间中一类混合映射不动点的Ishikawa迭代逼近问题

设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为Φ-强伪压缩映射.其中T=T1+T2,T1:K→K为Lipschitz映射,T2:K→K为具有有界值域映射.设{αn}n∞=0和{βn}n∞=0是0,1]中满足一定条件的两实数列.则Ishikawa迭代序列{xn}∞n=0强收敛于T的唯一不动点.

Ishikawa Iterative Approximation for Fixed Point with Mixed Mapping in Banach Spaces

Suppose that E is an uniformly smooth real Banach space,and K is a nonempty closed convex subset of E,T:K→K is Φ-strongly pseudocontrictive mapping,and T=T1+T2,T1:K→K is Lipschitz mapping,T2:K→K is a continuous mapping with the bounded range R(T).Let {αn}∞n=0 and {βn}∞n=0 be two real sequences in satisfying suitable conditions,then Ishikawa iterative process {xn}∞n=0 converges strongly to the unique fixed point of T.