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Caiping Yang, Songnian He, The successive contraction method for fixed points of pseudo-contractive mappings

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DOI: 10.23952/asvao.1.2019.3.07
Volume 1, Issue 3, 31 December 2019, Pages 337-347

 

Abstract. In this paper, a new general iterative method is proposed for finding a fixed point of a Lipschitz continuous pseudo-contractive mapping defined on a closed convex subset of a real Hilbert space. Since each iteration of our method can be reduced  to finding the fixed point of a strict contraction,  our iterative method  is called the successive contraction method. We give exact and inexact versions of the successive contraction method and prove their weak convergence, respectively. The main advantage of our method is that its convergence does not require the compactness assumption on  the operators  under consideration, which is quite different from the existing algorithms such as the Ishikawa iterative method. This superiority is also demonstrated by comparing the numerical performances of our method and the Ishikawa iteration process.

 

How to Cite this Article:
Caiping Yang, Songnian He, The successive contraction method for fixed points of pseudo-contractive mappings, Appl. Set-Valued Anal. Optim. 1 (2019), 337-347.