On Enriched Suzuki Mappings in Hadamard Spaces

Teodor Turcanu and Mihai Postolache ()
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Teodor Turcanu: Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
Mihai Postolache: Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 1, 1-11

Abstract: We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. More accurately, Hilbert spaces are particular Hadamard spaces, while enriched Suzuki nonexpansive mappings are natural generalizations of enriched nonexpansive mappings. Next, enriched Suzuki nonexpansive mappings naturally contain Suzuki nonexpansive mappings in Hadamard spaces. Besides technical lemmas, the results of this paper deal with (1) the existence of fixed points for enriched Suzuki nonexpansive mappings and (2) Δ and strong (metric) convergence of Picard iterates of the α -averaged mapping, which are exactly Krasnoselskij iterates for the original mapping.

Keywords: enriched Suzuki mapping; Hadamard space; fixed point; Picard iteration; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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