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Tauberian Conditions for Almost Convergence in a Geodesic Metric Space

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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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