Let C be a nonempty closed convex subset of a real Hilbert space H and \(T: C\rightarrow CB(H)\) be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping \(T: C\rightarrow Prox(H)\) is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.

让Ç是一个非空闭真实Hilbert空间的凸子集ħ和\（T：C \ RIGHTARROW CB（H）\）是一个多值Lipschitz伪非我映射。构建了Halpern–Ishikawa型迭代方案，并证明了该方案在适当条件下对T的固定点的强收敛性。此外，构造了一种逼近k严格伪压缩映射\（T：C \ rightarrow Prox（H）\）的固定点的迭代方法，并且在没有端点条件的情况下获得了该方法的强收敛性。本文获得的结果改进并扩展了文献中的已知结果。