An Implicit Iteration Process for Common Fixed Points of Two Infinite Families of Asymptotically Nonexpansive Mappings in Banach Spaces
نویسندگان
چکیده
F(T) ̸ = 0. As an important generalization of nonexpansive mappings, the class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] in 1972, who proved that if K is a nonempty, closed, and convex subset of a real uniformly convex Banach space and T : K → K is an asymptotically nonexpansive mapping, then T has a fixed point. Since then, iterative techniques for approximating fixed points of asymptotically nonexpansive mappings have been studied by various authors (see, e.g., [2–9]). However, these researches are all restricted to the situation of at most finite families of asymptotically nonexpansive mappings. For the extension of finite families to infinite ones, we develop an original method, namely, a specific way of choosing the indexes, for the iterative approximation of common fixed points of the involved mappings. We now cite an announced result as the object of our extension. In 2010, Wang et al. [10] constructed the following iteration process for two asymptotically nonexpansive mappings and obtained some strong convergence theorems for commonfixedpoints of the givenmappings inBanach spaces. For an arbitrary initial point x0 ∈ K, {xn}, {yn} are defined as follows:
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ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013