Strong convergence of iteration algorithms for a countable family of nonexpansive mappings
For a countable family \(\{T_n\}_{n=1}^{+\infty}\) of nonexpansive mappings, the authors consider the iteration \(x_{n+1}=\alpha_nu+(1-\alpha_n)T_nx_n\) under the conditions (C1) lim\(_{n\rightarrow \infty} \alpha _n=0\) and (C2) \(\sum_{n=1}^\infty \alpha _n = \infty\). These are called modified Halpern iterations by some authors and are referred to as Halpern type iterations in the present paper. The authors prove several strong convergence theorems for such iterations and present examples as well as applications to equilibrium problems and variational inequalities for continuous monotone mappings.
countable family of nonexpansive mappings
scientific article; zbMATH DE number 5586841
scientific article