Abstract
In this chapter we study the convergence of dynamic string-maximum methods for solving common fixed point problems in a space equipped with a generalized distance. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that our dynamic string-maximum algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.
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References
Butnariu, D., & Iusem, A. N. (2000). Totally convex functions for fixed points computation and infinite dimensional optimization. Dordrecht: Kluwer.
Reich, S., & Zaslavski, A. J. (2014). Genericity in nonlinear analysis. New York: Springer.
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Zaslavski, A.J. (2016). Spaces with Generalized Distances. In: Approximate Solutions of Common Fixed-Point Problems. Springer Optimization and Its Applications, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-33255-0_6
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DOI: https://doi.org/10.1007/978-3-319-33255-0_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33253-6
Online ISBN: 978-3-319-33255-0
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