Some novel approaches on the $(\overline{N},p,q)$ summability of double sequences of fuzzy numbers and its applications

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Arts and Sciences, Usak University, 64000, Usak, Turkey

2 Department of Mathematics, Faculty of Sciences, Ege University, 35100, Izmir, Turkey

Abstract

In this paper, our aim is to make a novel interpretation of relation between $(\overline{N},p,q)$ method and $P$-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling $O$-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from $(\overline{N},p,q)$ summability to $P$- convergence with some restrictions on the weight sequences. As special cases, we indicate that $O$-condition of Hardy type with respect to $(P_m)$ and $(Q_n)$ are Tauberian conditions for $(\overline{N},p,q)$ summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the $(\overline{N},p,q)$ summability method for fuzzy positive linear operators.

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Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 20, Issue 6
November and December 2023
Pages 105-122

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