The convergence property of Ishikawa iteration schemes in noncompact subsets of Hilbert spaces and its applications to complementarity theory
Let \(K\) be a closed convex subset of a Hilbert space and \(T:K \to K\) some nonexpansive map. Sufficient conditions are given for the Ishikawa iteration scheme \(x_{n+1}= (1-\alpha_n)x_n+\alpha_nT((1-\beta_n)x_n+\beta_nTx_n)\) to be convergent towards a fixed point of \(T\). Applications to complementarity theorems are also discussed.
variational inequalities as variational inclusions
scientific article; zbMATH DE number 2142425
scientific article