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Some novel approaches on the $(\overline{N},p,q)$ summability of double sequences of fuzzy numbers and its applications | ||
Iranian Journal of Fuzzy Systems | ||
دوره 20، شماره 6، بهمن و اسفند 2023، صفحه 105-122 اصل مقاله (245.73 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.44900.7922 | ||
نویسندگان | ||
Zerrin Onder* 1؛ Ekrem Savas1؛ Ibrahim Canak2 | ||
1Department of Mathematics, Faculty of Arts and Sciences, Usak University, 64000, Usak, Turkey | ||
2Department of Mathematics, Faculty of Sciences, Ege University, 35100, Izmir, Turkey | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Double sequences of fuzzy numbers؛ convergence in Pringsheim's sense؛ $(\overline{N}؛ p؛ q)$ summability؛ regularly varying sequences؛ slowly decreasing sequences؛ slowly oscillating sequences؛ weighted mean summability method؛ fuzzy Korovkin theory | ||
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