一类带混合误差项的增生算子方程的迭代解

Iterative Approximation of the Solution to a Class of Accretive Operator Equations with Mixed Errors

设 K是 Banach空间 E的非空凸有界子集 ,T:K→ K是一致连续强伪压缩的 ,{ αn} ,{ βn} ,{ un} ,{ vn}是满足一定条件的序列 ,则如下迭代序列 { xn}∞n=0 : x0 ∈ K ,yn=( 1 -βn) xn+βn Txn+ vn, n≥ 0 ,xn+1 =( 1 -αn) xn+αn Tyn+ un,n≥ 0强收敛于 T的不动点 .

Suppose K is a nonempty convex bounded subset of a Banach space E,Suppose T:K→K is a uniformly strong pseudo contraction and {α n}, {β n}, {u n}, {v n} are satisfying some conditions,then the sequence {x n} ∞ n=0 generated from an arbitrary x 0∈K by y n=(1-β n)x n+β nTx n+v n, n≥0, x n+1=(1-α n)x n+α nTy n+u n,n≥0 converges strongly to the fixed point of T.