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)≠∅. 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)=0 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).
Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm and F, K : be Lipschitz accretive maps with Suppose that the Hammerstein equation has a solution. An explicit iteration method is shown to converge strongly to a solution of the equation. No invertibility assumption is imposed on K and the operator F is not restricted to be angle-bounded. Our theorems are significant improvements on important recent results (e.g., (Chiume and Djitte, 2012)).
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