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Some conditions under which slow oscillation of a sequence of fuzzy numbers follows from Ces\`{a}ro summability of its generator sequence | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 3، دوره 11، شماره 4، آبان 2014، صفحه 15-22 اصل مقاله (335.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1621 | ||
| نویسنده | ||
| Ibrahim Canak* | ||
| Department of Mathematics, Ege University, 35100, Izmir, Turkey | ||
| چکیده | ||
| Let $(u_n)$ be a sequence of fuzzy numbers. We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces\`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces\`{a}ro summability method are established as particular cases. | ||
| کلیدواژهها | ||
| Ces\`{a}ro summability؛ Slow oscillation؛ Tauberian theorems؛ Sequences of fuzzy numbers | ||
| مراجع | ||
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\bibitem{alt1} Y. Alt{\i}n, M. Mursaleen and H. Alt{\i}nok, {\it Statistical summability (C,1) for sequences of fuzzy real numbers and a Tauberian theorem}, J. Intell. Fuzzy Syst., {\bf 21}\textbf{(6)} (2010), 379--384. \bibitem{alt2} H. Alt{\i}nok and M. Mursaleen, {\it $\Delta$-Statistically boundedness for sequences of fuzzy numbers}, Taiwanese J. Math., {\bf 15}\textbf{(5)} (2011), 2081--2093. \bibitem{col} R. \d{C}olak, Y. Alt{\i}n and M. Mursaleen, {\it On some sets of difference sequences of fuzzy numbers}, Soft Comput., {\bf 15}\textbf{(4)} (2011), 787--793 \bibitem{dub} D. Dubois and H. Prade, {\it Fuzzy numbers: An overview, Analysis of Fuzzy Information, vol. 1}, Mathematical Logic, CRC Press, Boca, FL, 1987, 3--39. \bibitem{dut} A. J. Dutta and B. C. Tripathy, {\it On $I$-acceleration convergence of sequences of fuzzy real numbers}, Math. Model. Anal., {\bf 17}\textbf{(4)} (2012), 549--557. \bibitem{fas} H. Fast, {\it Sur la convergence statistique}, Colloq. Math, {\bf 2} (1951), 241--244. \bibitem{har} G. H. Hardy, {\it Divergent Series}, 2nd ed., New York, NY, 1991. \bibitem{mat} M. Matloka, {\it Sequences of fuzzy numbers}, BUSEFAL, {\bf 28} (1986), 28--37. \bibitem{mor} F. M\'{o}ricz, {\it Necessary and sufficient Tauberian conditions, under which convergence follows from summability $(C,1)$}, Bull. London Math. Soc., {\bf 26} (1994), 288--294. \bibitem{mor2} F. M\'{o}ricz, {\it Ordinary convergence follows from statistical summability $(C,1)$ in the case of slowly decreasing or oscillating sequences}, Colloq. Math., {\bf 99}\textbf{(2)} (2004), 207--219. \bibitem{nan} S. Nanda, {\it On sequences of fuzzy numbers}, Fuzzy Sets and Systems, {\bf 33}\textbf{(1)} (1989), 123--126. \bibitem{sch} I. J. Schoenberg, {\it The integrability of certain functions and related summability methods}, Amer. Math. Monthly, {\bf 66} (1959) 361--375. \bibitem{sub} P. V. Subrahmanyam, {\it Ces\`{a}ro summability of fuzzy real numbers}, J. Anal., {\bf 7} (1999), 159--168. \bibitem{tal} \"{O}. Talo and C. \d{C}akan, {\it On the Ces\`{a}ro convergence of sequences of fuzzy numbers}, Appl. Math. Lett., {\bf 25} (2012), 676--681. \bibitem{tri} B. C. Tripathy and A. Baruah, {\it N\"{o}rlund and Riesz mean of sequences of fuzzy real number}, Appl. Math. Lett., {\bf 23}\textbf{(5)} (2010), 651--655. \bibitem{tri1} B. C. Tripathy and A. Baruah, {\it Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers}, Kyungpook Math. J., {\bf 50}\textbf{(4)} (2010), 565--574. \bibitem{tri3} B. C. Tripathy, A. Baruah, M. Et and M. G\"{u}ng\"{o}r, {\it On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers}, Iran. J. Sci. Technol. Trans. A Sci., {\bf 36}\textbf{(2)} (2012), 147--155. \bibitem{tri2} B. C. Tripathy and S. Borgohain, {\it Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function}, Adv. Fuzzy Syst., Art. ID 216414, (2011), 6. \bibitem{tri5} B. C. Tripathy and S. Debnath, {\it On generalized difference sequence spaces of fuzzy numbers}, Acta Scientiarum Technology, {\bf 35}\textbf{(1)} (2013), 117--121. \bibitem{tri4} B. C. Tripathy and A. J. Dutta, {\it Lacunary bounded variation sequence of fuzzy real numbers}, J. Intell. Fuzzy Systems, {\bf 24}\textbf{(1)} (2013), 185--189. \bibitem{zad} L. A. Zadeh, Fuzzy sets, {\it Information and Control}, {\bf 8} (1965), 338--353. | ||
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