Banach空间有限个极大单调算子公共零点的迭代强收敛定理

令E为实光滑、一致凸Banach空间,E为其对偶空间.令Ai E×E,i=1,2,…,m,为极大单调算子且∩mi=1Ai-10≠.将引进一个新定义、给出一种新迭代算法,并利用Lyapunov泛函与广义投影算子等技巧,证明迭代序列强收敛于Ai的公共零点,i=1,2,…,m.去掉了以往结论中过强的限定条件,是对笔者以往工作的延续。

Strong Convergence Iterative Theorem of Common Zero Points for Finite Maximal Monotone Operators in Banach Spaces

Let E be a real smooth and uniformly convex Banach space with E* its duality space.For i=1,2,…,m,let AiE×E* be maximal monotone operators with ∩mi=1A-1i0≠φ.A new definition and a new iterative scheme are introduced and the result that the iterative sequence is strongly convergent to common zero points of maximal monotone operators Ai(i=1,2,…,m) is obtained by using the techniques of Lyapunov functional and generalized projection operator,etc.Some stronger restrictions imposed on the iterative sequence before are omitted and the result is a continuation of our previous work.