Convergence Theorems for Fixed Points of Multivalued Mappings in Hilbert Spaces

摘要

LetHbe a real Hilbert space andKa nonempty closed convex subset ofH. SupposeT:K→CB(K)is a multivalued Lipschitz pseudocontractive mapping such thatF(T)≠∅. An Ishikawa-type iterative algorithm is constructed and it is shown that, for the corresponding sequence{xn}, under appropriate conditions on the iteration parameters,lim infn→∞⁡ d (xn,Txn)=0holds. Finally, convergence theorems are proved under approximate additional conditions. Our theorems are significant improvement on important recent results of Panyanak (2007) and Sastry and Babu (2005).