令E为实一致光滑Banach空间,A:D(A)=E→2E为m增生映射,z∈E为任意元,0∈R(A).序列{xn}(∪)D(A)定义为xn+1=xn-λn(un+θn(xn-z)+en),其中un∈Axn,(A)n≥1,这里{λn}和{θn}为满足一定条件的正实数列,则xn→x*∈A-10.本质上将Chidume和Zegeye关于m增生映射零点的精确迭代格式推广为带误差项的形式.
[1] BRUCK R E. A strongly convergent iterative solution of 0∈U(x) for a maximal monotone operator U in Hilbert space [J]. Journal of Mathematical Analysis and Applications 1974, 48.
[2] Kamimura S., Takahashi W.. Approximating solutions of maximal monotone operators in Hilbert spaces [J]. Journal of Approximation Theory 2000, 2(2).
[3] Osilike MO.. APPROXIMATION METHODS FOR NONLINEAR M-ACCRETIVE OPERATOR EQUATIONS [J]. Journal of Mathematical Analysis and Applications 1997, 1(1).
[4] CHIDUME C E, ZEGEGYE H. Iterative solution of 0∈Ax for an m-accretive operator A in certain Banach spaces [J]. Journal of Mathematical Analysis and Applications 2002, 269.
[5] XU Z B, ROACH G F. Characteristic inequalities for uniformaly convex and uniformly smooth Banach spaces [J]. Journal of Mathematical Analysis and Applications 1991, 157.
[6] REICH S. Strong convergence theorems for resolvents of accretive operators in Banach spaces [J]. Mathematics Analysis and Applications 1980, 75.
