Abstract
We introduce a new two‐step iterative scheme for two asymptotically nonexpansive nonself‐mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).
Highlights
Let E be a real normed space and K be a nonempty subset of E
We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonselfmappings in a uniformly convex Banach space
A mapping T : K → K is called nonexpansive if T x − T y ≤ x − y for all x, y ∈ K
Summary
Let E be a real normed space and K be a nonempty subset of E. The asymptotically nonexpansive nonself-mapping is defined as follows. A nonself mapping T : K → E is called asymptotically nonexpansive if there exists sequence {kn} ⊂ 1, ∞ , kn → 1 n → ∞ such that
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