Common Fixed Points of Operators with Property (E) in CAT(0) Spaces

Andreea Bejenaru and Cristian Ciobanescu
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Andreea Bejenaru: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Cristian Ciobanescu: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 3, 1-16

Abstract: This paper features the search for common fixed points of two operators in the nonlinear metric setting provided by CAT(0) spaces. The analysis is performed for the generalized nonexpansivity condition known as condition (E), Garcia-Falset et al., and relies on the three step iteration procedure S n by Sintunavarat and Pitea. The convergence analysis reveals the approximate solutions as limit points for an iteration sequence, where both the nonexpansive mappings to be analyzed and the specific curved structure of the framework interfere. To point out properly the meaning of this approach, we provide also examples accompanied by numerical simulations. The Poincaré half-plane is one of the non-positively curved setting to be used.

Keywords: CAT(0) space; S n iteration; condition (E); Poincaré half-plane (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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