Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
By Shih-sen Chang, Jong Kyu Kim, Xiongrui Wang. 2010
132 citations recorded by the source corpus.
The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/e22e14c15ba6ceefb04100559bbaf3b6a12ad241
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In Computational Theory and Mathematics
In Geometry and Topology
In Numerical Analysis
Citations in the corpus
- Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems (2015, background): “The reader is referred to [6, 16] for examples of closed and asymptotically quasi φ-nonexpansive mappings.”
- Parallel and sequential hybrid methods for a finite family of asymptotically quasi $$\phi $$ϕ-nonexpansive mappings (2015, background): “Lemma 4 [5,15,21] Let E be a strictly convex reflexive smooth Banach space, A be a maximal monotone operator of E into E∗, and Jr = (J + r A)−1 J : E → D(A) be the resolvent of A with r > 0.”