△-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces. (20th March 2013) - Shi, Luo Yi; Chen, Ru Dong; Wu, Yu Jing
Abstract : New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mappingT of a closed convex subsetC of a CAT(0) spaceX . Consider the iteration process x n , wherex 0 ∈ C is arbitrary andx n + 1 = α n x n ⊕ ( 1 - α n ) T n y n orx n + 1 = α n T n x n ⊕ ( 1 - α n ) y n, y n = β n x n ⊕ ( 1 - β n ) T n x n forn ≥ 1, where α n , β n ⊂ ( 0, 1 ) . It is shown that under certain appropriate conditions onα n, β n, x n △-converges to a fixed point ofT .