Construction of common fixed points of a countable family of λλ-demicontractive mappings in arbitrary Banach spaces

We propose iterative Mann-type schemes to approximate a common fixed point of a countable family of λλ-demicontractive and L-Lipschitzain mappings. This improves the recent result of Chidume et al. [C.E. Chidume, M. Abbas, Bashir Ali, Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings. Appl. Math. Comput. 194(1) (2007) 1–6] from a single strictly pseudocontractive mapping to a family of more general mappings.