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On Enriched Suzuki Mappings in Hadamard Spaces

Author

Listed:
  • Teodor Turcanu

    (Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Mihai Postolache

    (Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
    The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, Health Big Data Research Institute, North Minzu University, Yinchuan 750021, China
    Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Teodor Turcanu & Mihai Postolache, 2024. "On Enriched Suzuki Mappings in Hadamard Spaces," Mathematics, MDPI, vol. 12(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:157-:d:1312649
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