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Weighted λ-statistical convergence connecting a statistical summability of sequences of fuzzy numbers and Korovkin-type approximation theorems

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Abstract

In this paper, we investigated the notion of generalized weighted λ-statistical convergence connecting \( \left( {\bar{N}_{\lambda } , p_{n} } \right)^{F} \)-statistical summability of sequences of fuzzy numbers. Some inclusion relations and other related results for the new summability methods are also given. Furthermore, we give a Korovkin-type approximation theorem for fuzzy positive linear operators using the notion of generalized weighted \( \left( {\bar{N}_{\lambda } , p_{n} } \right)^{F} \)-statistical summability.

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Acknowledgements

The authors are grateful to the anonymous referees for their constructive comments which were helpful to improve the manuscript.

Funding

This study was funded by University Grants Commission (UGC), New Delhi, India (grant number: F./2015-16/NFO-2015-17-OBC-ASS-36722/(SA-III/Web site)).

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Authors and Affiliations

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

    Hemen Dutta & Jyotishmaan Gogoi

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  1. Hemen Dutta
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  2. Jyotishmaan Gogoi
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Correspondence to Hemen Dutta.

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Dutta, H., Gogoi, J. Weighted λ-statistical convergence connecting a statistical summability of sequences of fuzzy numbers and Korovkin-type approximation theorems. Soft Comput 23, 12883–12895 (2019). https://doi.org/10.1007/s00500-019-03846-2

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