Banach空间中有限个极大单调算子公共零点的迭代格式

令E为实光滑、一致凸Banach空间,E~*为其对偶空间．令A_i,B_i (?) E×E~*,i= 1,2,…,m,为极大单调算子且(?)(A_i~(-1)0∩B_i~(-1)0)≠φ．引入新的迭代算法,并利用Lyapunov泛函,Q_r算子与广义投影算子等技巧,证明迭代序列弱收敛于极大单调算子A_i,B_i,i= 1,2,…,m的公共零点的结论．

Iterative Scheme of Common Zero Points for Finite Maximal Monotone Operators in Banach Space

Let $E$ be a real smooth and uniformly convex space with $E^* $its duality space. For $i = 1,2,\cdots, m,$ let $A_i,B_i \subset E \times E^*$ be maximal monotone operators with $\mathop{\bigcap}\limits_{i=1}^{m}(A^{-1}_{i}0\bigcap B_{i}^{-1}0)\\\neq \emptyset $. A new iterative scheme is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators $A_i$ and $B_i ,i = 1,2,\cdots,m $ by using the techniques of Lyapunov functionals, $Q_r$ operators, and generalized projection operators, etc.