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Cesàro summability of sequences in intuitionistic fuzzy normed spaces and related Tauberian theorems

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Abstract

We define the concept of Cesàro summability method in intuitionistic fuzzy normed spaces and prove a related Tauberian theorem. Also, we define slowly oscillating sequences in intuitionistic fuzzy normed spaces, prove related theorems and show that Cesàro summability of slowly oscillating sequences implies ordinary convergence in intuitionistic fuzzy normed spaces. Finally, we give an analogue of classical two-sided Tauberian theorem due to Hardy by using the concept of q-boundedness.

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Acknowledgements

We thank the reviewers for his/her careful reading and constructive criticism of the earlier version of this paper which improved the presentation and its readability.

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Authors and Affiliations

  1. Manisa Celal Bayar Üniversitesi Küme Evleri, 45140, Yunusemre, Manisa, Turkey

    Özer Talo

  2. Department of Mathematics, Manisa Celal Bayar University, Manisa, Turkey

    Enes Yavuz

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  1. Özer Talo
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  2. Enes Yavuz
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Correspondence to Enes Yavuz.

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Talo, Ö., Yavuz, E. Cesàro summability of sequences in intuitionistic fuzzy normed spaces and related Tauberian theorems. Soft Comput 25, 2315–2323 (2021). https://doi.org/10.1007/s00500-020-05301-z

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