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Statistical \((C,1)(E,\mu )\)-summability and associated fuzzy approximation theorems with statistical fuzzy rates

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Abstract

The concept of statistical convergence has attracted the pervasive attention of the current researchers due basically to the fact that it is stronger than the ordinary convergence. Korovkin-type approximation theorem plays a vital role in the convergence of sequences of positive linear operators. Moreover, this type of approximation theorems has been extended through different statistical summability methods over general sequence spaces. The paper investigated statistical \((C,1)(E,\mu )\) product summability mean for sequences of fuzzy numbers and proved a fuzzy Korovkin-type approximation theorem. Furthermore, we have established another result for the fuzzy rate of convergence which is uniform in fuzzy Korovkin-type approximation theorem under our proposed summability mean.

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Authors and Affiliations

  1. Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    A. A. Das, S. K. Paikray & T. Pradhan

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

    Hemen Dutta

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  1. A. A. Das
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  2. S. K. Paikray
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  3. T. Pradhan
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  4. Hemen Dutta
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Correspondence to Hemen Dutta.

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Das, A.A., Paikray, S.K., Pradhan, T. et al. Statistical \((C,1)(E,\mu )\)-summability and associated fuzzy approximation theorems with statistical fuzzy rates. Soft Comput 24, 10883–10892 (2020). https://doi.org/10.1007/s00500-019-04591-2

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