Abstract
In this chapter we study the convergence of iterative methods for solving common fixed point problems in a metric space. Our main goal is to obtain an approximate solution of the problem using perturbed algorithms. We show that the inexact iterative method generates an approximate solution if perturbations are summable. We also show that if the mappings are nonexpansive and the perturbations are sufficiently small, then the inexact method produces approximate solutions.
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References
Bacak M (2014) Convex analysis and optimization in Hadamard spaces. De Gruyter series in nonlinear analysis and applications. De Gruyter, Berlin
Zaslavski AJ (2017) Asymptotic behavior of two algorithms for solving common fixed point problems. Inverse Prob 33:1–15
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Zaslavski, A.J. (2018). Iterative Methods in Metric Spaces. In: Algorithms for Solving Common Fixed Point Problems. Springer Optimization and Its Applications, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-319-77437-4_2
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DOI: https://doi.org/10.1007/978-3-319-77437-4_2
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-77437-4
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