The Iterative Construction of Common Zero Points for a Family of Maximal Monotone Operators in Banach Space

@inproceedings{Li2010TheIC,
  title={The Iterative Construction of Common Zero Points for a Family of Maximal Monotone Operators in Banach Space},
  author={Wei Li},
  year={2010}
}
Let E be a real smooth and uniformly convex Banach space with E* its duality space.Let AiE×E*,i=1,2,…,m be maximal monotone operators and there exists i0∈{1,2,…,m} such that φ≠A-1i0(0)∩mi=1i≠i0 A-1i(0).A new accurate iterative algorithm and a new proximate algorithm are introduced which are proved to be strongly convergent to common zero points of maximal monotone operators{Ai}mi=1 by using the techniques of Lyapunov functional.