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Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem

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Abstract

The paper aims to investigate different types of weighted statistical convergence and weighted statistical summability of double sequences of fuzzy numbers. Relations connecting statistical convergence and statistical summability have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. Relevant inclusion relations and related results concerning the new fuzzy summability methods have also been examined in detail. Finally, a Korovkin-type approximation theorem for double sequences of fuzzy positive linear operators has been established using the most generalized version of the summability method and showed its efficiency by means of a concrete example.

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Acknowledgements

The authors are grateful to the learned referees for their constructive comments and suggestions.

Funding

This study was funded by University Grants Commission (UGC), New Delhi, India (Grant no.: F./2015-16/NFO-2015-17-OBC-ASS-36722/(SA-III/Website)).

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Authors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, 781014, Assam, India

    Jyotishmaan Gogoi & Hemen Dutta

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  1. Jyotishmaan Gogoi
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  2. Hemen Dutta
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Contributions

Author 2 suggested the topic of the paper to Author 1 first with some hints. Author 1 then prepared the very fast draft and presented to Author 2 for initial assessment. Both authors then developed the main results to their current form after several discussions and read and approved the manuscript for publication.

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Correspondence to Hemen Dutta.

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Gogoi, J., Dutta, H. Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem. Soft Comput 25, 7645–7656 (2021). https://doi.org/10.1007/s00500-021-05724-2

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