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Fuzzy approximation theorems via power series summability methods in two variables

  • Fuzzy systems and their mathematics
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Abstract

This paper contains a power series summability method based on Korovkin type approximation theorem for a sequence of fuzzy positive linear operators in two variables. Besides that, a theorem related to fuzzy rate of convergence has been derived with the help of fuzzy modulus of continuity, which gives clarity to understanding the analogous observations between fuzzy set theory and classical theory. Additionally, an example is illustrated which gives a better idea to understand that summability in two variable-based Korovkin type theorem has less drawback over fuzzy set theory.

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable suggestions and comments.

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We did not receive any sort of funding to report the study.

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  1. Digvijay Singh and Karunesh Kumar Singh are contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Sciences and Humanities, Institute of Engineering and Technology, Dr. A.P.J. Abdul Kalam Technical University, Lucknow, Uttar Pradesh, 226021, India

    Digvijay Singh & Karunesh Kumar Singh

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  1. Digvijay Singh
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  2. Karunesh Kumar Singh
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Correspondence to Karunesh Kumar Singh.

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Singh, D., Singh, K.K. Fuzzy approximation theorems via power series summability methods in two variables. Soft Comput 28, 945–953 (2024). https://doi.org/10.1007/s00500-023-09378-0

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