Banach空间中含Lipschitz强增生 算子的算子方程之构造可解性

CONSTRUCTIVE SOLVABILITY OF OPERATOR EQUATIONS WITH LIPSCHITZIAN STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

设X为实一致光滑Banach空间，A：X→X为Lipschitz 强增生算子，设L≥1和k∈(0,1)分别为A的Lipschitz常数与强增生常数。设｛tn｝ n≥0为(0，1］中的实数列满足条件：(i)tn→0(n→∞)；，迭代地定义序列｛xn｝n≥0如下：

Let X be a real uniformly smooth Banach space and let A:X→ X be a Lipschitzian and φ-strongly accretive operator such that .Let ｛tn｝n≥0 be a real sequence in (0, 1］ satisfying conditions:(i)tn→0 as n→∞;(ii)∑∞n=0tn=∞.For arbitrary given f in X and initial value x0∈X，define iteratively a sequence ｛xn｝n≥0 as follows: