Unveiling Cesà ro summability under neutrosophic 2-norms
DOI:
https://doi.org/10.5269/bspm.76593Resumen
This paper introduces the concepts of Cesà ro summability within the framework of neutrosophic 2-normed spaces (N2-NS). We establish that Cesà ro summability does not necessarily imply ordinary convergence with regard to neutrosophic 2-norm, providing a concrete example to illustrate this distinction. In this connection, we prove necessary and sufficient condition for the sequences in N2-NS that their Cesà ro summability guarantees ordinary convergence.
Referencias
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13. Sahiner, A., Gurdal, M., Saltan, S. and Gunawan, H., Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5), 1477-1484, (2007).
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2. Fradkov, A. L. and Evans, R. J., Control of chaos: Methods and applications in engineering, Annu. Rev. Control, 29(1), 33-56, (2005).
3. Gahler, S. 2-normed spaces, Math. Nachr., 28, 1-43, (1964).
4. Hong, L. and Sun, J. Q., Bifurcations of fuzzy nonlinear dynamical systems, Commun. Nonlinear Sci. Numer. Simul., 11(1), 1-12, (2006).
5. Klement, E. P., Mesiar, R. and Pap, E., Triangular norms. Position paper I: basic analytical and algebraic properties, Fuzzy Sets Syst., 143, 5-26, (2004).
6. Kirisci, M. and Simsek, N., Neutrosophic normed spaces and statistical convergence, J. Anal., 28, 1059-1073, (2020).
7. Kisi, O., Ideal convergence of sequences in neutrosophic normed spaces, J. Intell. Fuzzy Syst., 41(2), 2581-2590, (2021).
8. Khan, V. A., Khan, M. D. and Ahmad, M., Some new type of lacunary statistically convergent sequences in neutrosophic normed space, Neutrosophic Sets Syst., 42, 241-252, (2021).
9. Murtaza, S., Sharma, A. and Kumar, V., Neutrosophic 2-normed spaces and generalized summability, Neutrosophic Sets Syst., 55(1), Article 25, (2023).
10. Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific J. Math., 10(1), 313-334, (1960).
11. Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure. Appl. Math., 24, 287-297, (2005).
12. Saadati, R. and Park, J. H., On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals, 27(2), 331-344, (2006).
13. Sahiner, A., Gurdal, M., Saltan, S. and Gunawan, H., Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5), 1477-1484, (2007).
14. Talo, O. and Basar, F., Necessary and sufficient Tauberian conditions for the Ar method of summability, Math. J. Okayama Univ., 60, 209-219, (2018).
15. Zadeh, L. A. Fuzzy sets, Inform. control, 8, 338-353, (1965).
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2025-08-13
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