一致凸Banach空间中增殖算子方程f∈x+Tx的迭代解

THE ITERATIVE SOLUTION OF THE EQUATION F∈X+TX FOR ACCRETIVE OPERATOR T IN UNIRORMLY CONVEX BANACH SPACES

设X是其对偶X~*为一致凸的Banach空间,T是开域D(T)(?)X上的增殖算子。如果X~*的凸性模满足δ_x~*(ε)≥C_ε~P((P≥2),Sx=f-Tx,则S的Mann迭代程序(T是多值时,Cn=1/(n+r),r>0,T是单值局部李普希兹映射时,Cn=λ,0<λ<1)收敛于方程f∈x+Tx的解。这些结果改进和推广了Bruck、Chidume的结果。

Let X be a Banach Space with a uniformly Convex dual X~*, T a accretive operator with open domain D(T)(?)X. If modulus of convexity of X~* satisfies δ_(x~*)(ε)≥сε~p (p≥2), Sx=f-Tx, then Mann iterative process (when T is a multivalued, C_n=1/(n+r)n>0, T a single valued locally Lipschitzian, c_n=λ, 0<λ<1) of S converge to a solution of f∈x+Tx. The results improve and generalize the corresponding results of Bruck, Chidume.