Another control condition in an iterative method for nonexpansive mappings

By Hong-Ku N Xu. Bulletin of the Australian Mathematical Society, 2002

367 citations recorded by the source corpus.

We prove the convergence of an iterative method to a fixed point of a nonexpansive mapping in a uniformly smooth Banach space. We are able to relax one of the control conditions of P.L. Lions (1977).

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/115029a9fc59a9dbe6977629b9515f336a9c6137

Citations in the corpus

• TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN’S TYPE IN HILBERT SPACES AND APPLICATIONS (2012, neutral): “([2, 28]).”
• Minimum-norm solution of variational inequality and fixed point problem in banach spaces (2015, neutral): “9 [29] Let {an} be a sequence of nonnegative real numbers satisfying the following relation: an+1 ≤ (1 − αn)an + αnδn, n ≥ n0, where {αn} ⊂ (0, 1) and {δn} ⊂ R satisfying the following conditions: limn→∞ αn = 0, ∑∞ n=1 αn = ∞, and limn→∞ δn ≤ 0.”
• Strong convergence theorem for a common point of solution of variational inequality and fixed point problem (2012, neutral): “[18] Let { a n } be a sequence of nonnegative real numbers satisfying the following relation: where { β n } ⊂ (0 , 1) and { δ n } ⊂ R satisfying the following conditions: lim Lemma 2.10.”