Banach空间中有限个极大单调算子公共零点的迭代格式

ITERATIVE SCHEME OF COMMON ZERO POINTS FOR FINITE MAXIMAL MONOTONE OPERATORS IN BANACH SPACE

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．

Let E be a real smooth and uniformly convex space with E~＊its duality space. For i=1,2,…,m,let Ai,Bi E×E^＊ be maximal monotone operators with∩i=1^m（Ai^-10∩Bi^-10）≠φ.A new iterative scheme is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators Ai and Bi,i=1,2,…,m by using the techniques of Lyapunov functionals,Qr operators,and generalized projection operators,etc.