Abstract
In this article we study different properties of convergent, null and bounded sequence spaces of fuzzy real numbers defined by an Orlicz function, like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results, too.
[1] DAS, N. R.— DAS, P.— CHOUDHURY, A.: Absolute value like fuzzy real number and fuzzy real-valued sequence spaces, J. Fuzzy Math. 4 (1996), 421–433. Search in Google Scholar
[2] KALEVA, O.— SEIKKALA, S.: On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), 215–229. http://dx.doi.org/10.1016/0165-0114(84)90069-110.1016/0165-0114(84)90069-1Search in Google Scholar
[3] KAMTHAN, P. K.— GUPTA, M.: Sequence Spaces and Series. Lecture Notes in Pure and Appl. Math. 65, Marcel Dekker, Inc., New York-Basel, 1981. Search in Google Scholar
[4] KRASNOSELKII, M. A.— RUTITSKY, Y. B.: Convex Functions and Orlicz Spaces, P. Noordhoff, Groningen, 1961. Search in Google Scholar
[5] LINDENSTRAUSS, J.— TZAFRIRI, L.: On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379–390. http://dx.doi.org/10.1007/BF0277165610.1007/BF02771656Search in Google Scholar
[6] NAKANO, H.: Modular sequence spaces, Proc. Japan Acad. Ser. A Math. Sci. 27 (1951), 508–512. 10.3792/pja/1195571225Search in Google Scholar
[7] PARASHAR, S. D.— CHOUDHARY, B.: Sequence spaces defined by Orlicz function, Indian J. Pure Appl. Math. 25 (1994), 419–428. Search in Google Scholar
[8] RATH, D.— TRIPATHY, B. C.: Matrix maps on sequence spaces associated with sets of integers, Indian J. Pure Appl. Math. 27 (1996), 197–206. Search in Google Scholar
[9] SAVAS, E.: A note on sequence of fuzzy numbers, Inform. Sci. 124 (2000), 297–300. http://dx.doi.org/10.1016/S0020-0255(99)00073-010.1016/S0020-0255(99)00073-0Search in Google Scholar
[10] SAVAS, E.— RHOADES, B. E.: On some new sequence spaces of invariant means defined by Orlicz functions, Math. Inequal. Appl. 5 (2002), 271–281. Search in Google Scholar
[11] SUBRAHMANYAM, P. V.: Cesàro summability for fuzzy real numbers, J.Anal. 7 (1999), 159–168. Search in Google Scholar
[12] TRIPATHY, B. K.— NANDA, S.: Absolute value of fuzzy real numbers and fuzzy sequence spaces, J. Fuzzy Math. 8 (2000), 883–892. Search in Google Scholar
[13] TRIPATHY, B. C.— ET, M.— ALTIN, Y.: Generalized difference sequence spaces defined by Orlicz functions in a locally convex space, J. Anal. Appl. 1 (2003), 175–192. Search in Google Scholar
© 2008 Mathematical Institute, Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
