Robustness of Theta Method for Nonexpansive Mappings
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In this paper, we approximate fixed points of nonexpansive mappings in Hilbert spaces using an implicit method. More precisely, we study weak and strong convergence results for \(\theta\)-method with small perturbations. Some illustrative examples and numerical computations show the usefulness of our theorems. We also present an application of our results to integral equations.
KeywordsNonexpansive mapping Theta method Nearest projection
Mathematics Subject ClassificationPrimary 47H10 47H09 47J05 47J25 54H25
We are very much thankful to the reviewers for their constructive comments and suggestions which have been useful for the improvement of this paper.