Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings
C.E. Chidume, Jinlu Li, Aniefiok Udomene · Proceedings of the American Mathematical Society · 2004
Let E E be a real Banach space with a uniformly Gâteaux differentiable norm possessing uniform normal structure, K K be a nonempty closed convex and bounded subset of E E , T : K ⟶ K T: K \longrightarrow K be an asymptotically nonexpansive mapping with sequence { k n } n ⊂ [ 1 , ∞ ) \{k_n\}_n\subset [1, \infty ) . Let u ∈ K u\in K be fixed, { t n } n ⊂ ( 0 , 1 ) \{t_n\}_n \subset (0, 1) be such that lim n → ∞ t n = 1 \lim \limits _{n\to \infty }t_n = 1 , t n k n > 1 t_nk_n > 1 , and lim n → ∞