An implicit iteration process for common fixed points of two infinite families of asymptotically nonexpansive mappings in Banach spaces. (English) Zbl 1266.47090
Summary: Let be a nonempty, closed, and convex subset of a real uniformly convex Banach space . Let and be two infinite families of asymptotically nonexpansive mappings from to itself with , . For an arbitrary initial point , is defined as follows: , , , where and with and satisfying the positive integer equation: , ; and are two countable subsets of and , respectively; , , , , , and are sequences in for some , satisfying and . Under some suitable conditions, a strong convergence theorem for common fixed points of the mappings and is obtained. The results extend those of the authors whose related works are restricted to the situation of finite families of asymptotically nonexpansive mappings.
|47J25||Iterative procedures (nonlinear operator equations)|
|47H09||Mappings defined by “shrinking” properties|