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Tauberian Conditions for Almost Convergence in a Geodesic Metric Space

Abstract

In the present paper, after recalling the Karcher mean in Hadamard spaces, we study the relation between convergence, almost convergence and mean convergence (respect to the defined mean) of a sequence in Hadamard spaces. These results extend Tauberian conditions from Banach spaces to Hadamard spaces. Also, we show that every almost periodic sequence in Hadamard spaces is almost convergent.

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Acknowledgements

The authors are grateful to the referees for their careful reading and valuable comments and suggestions.

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Correspondence to Hadi Khatibzadeh.

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Khatibzadeh, H., Pouladi, H. Tauberian Conditions for Almost Convergence in a Geodesic Metric Space. Results Math 75, 43 (2020). https://doi.org/10.1007/s00025-020-1169-6

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Keywords

  • Taubrerian conditions
  • geodesic metric space
  • mean
  • almost convergence
  • almost periodicity

Mathematics Subject Classification

  • 40A05
  • 40A30