Convergence Theorems for Fixed Points of Multivalued Mappings in Hilbert Spaces

Let H be a real Hilbert space and K a nonempty closed convex subset of H. Suppose T: K -> CB(K) is a multivalued Lipschitz pseudocontractive mapping such that F(T) not equal 0. An Ishikawa-type iterative algorithm is constructed and it is shown that, for the corresponding sequence {x(n)}, under appropriate conditions on the iteration parameters, lim inf(n -> infinity) d(x(n) , Tx(n)) holds. 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).