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Chang, Shih-sen; Zhao, Liangcai; Liu, Min; Tang, Jinfang

Convergence theorems for total asymptotically nonexpansive mappings in \(\mathrm{CAT} (\kappa)\) spaces. (English) Zbl 1541.54030

Fixed Point Theory Algorithms Sci. Eng. 2023, Paper No. 2, 14 p. (2023).
Summary: The purpose of this paper is to study the convergence theorems in \(\operatorname{CAT} (\kappa )\) spaces with \(k > 0\) for total asymptotically nonexpansive mappings which are essentially wider than nonexpansive mappings, asymptotically nonexpansive mapping, and asymptotically nonexpansive mappings in the intermediate sense. Our results generalize, unify, and improve several comparable results in the existing literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Keywords:

total asymptotically nonexpansive mappings; \(\mathrm{CAT} (\kappa)\) space; \(k > 0\); demiclosedness principle; asymptotically nonexpansive mapping in the intermediate sense; asymptotically nonexpansive mapping; \(\Delta\)-convergence; strong convergence
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References:

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