摘要
设X为一致光滑Banach空间,A:D（A） X→X为K-正定算子满足D（A）=D（K）,则存在常数β>0使得 x∈D（A）,||Ax||≤β||Kx||而且 f∈X,方程∧x=f有唯一解;设{an}n≥0为[0,1]中的实数列满足（i）an→0（n→∞）,（ii）sum from n=0 to ∞ an=∞, x0∈D（A）,迭代地定义序列{xn}n≥0如下:则{xn}n≥0强收敛于方程Ax=f的唯一解.
Let X be a uniformly smooth Banach space and let A:D(A) X→X be a K-positive definite operator with D(A) = D(K) . Then there exists a constant β>0 such that for every x∈D(A) , ||Ax||≤β||Kx||. Furthermore, the operator A is closed, R(A) = A , and the equation Ax =f , for each f∈X, has a uniqne solution. Let {an}n≥0 be a real sequence in [0,1] satisfying conditions; (i)an→0(n→∞); and (ii)sum from n=0 to ∞ an=∞. Define the sequence {xm}n>0 iteratively byThen the sequence {xn}n≥0 defined by ( * ) converges strongly to the unique solution of the e-quation Ax = f in X .
