Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers
Authors: N. Subramanian, U. K. Misra, M. S. Panda
Abstract:
In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.Keywords: Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331079
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1926References:
[1] S.Aytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci., 165(2004), 129-138.
[2] M.Basarir and M.Mursaleen, Some sequence spaces of fuzzy numbers generated by infinite matrices, J. Fuzzy Math., 11(3)(2003), 757-764.
[3] T.Bilgin, Δ−statistical and strong Δ−Ces'aro convergence of sequences of fuzzy numbers,Math. Commun., 8(2003), 95-100.
[4] P.Diamondand P.Kloeden, Metric spaces of fuzzy sets, Fuzzy sets Syst., 35(1990), 241-249.
[5] Jin-xuan Fang and Huan Huang, On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Syst., 147(2004), 417-435.
[6] H.Fast, Surla convergence statistique, Colloq. Math., 1951, 241-244.
[7] J.Fridy, On the statistical convergence, Analysis, 5(1985), 301-313.
[8] L.Leindler, ¨U ber die Vallee-Pousinsche Summierbarkeit Allgemeiner Orthogonalreihen, Acta Math Acad. Sci. Hungar., 16(1965), 375-387.
[9] J.S.Kwon, On Statistical and P-Ces`aro convergence of fuzzy numbers, Korean J. Compu. Appl. math. 7(1) (2000), 195-203.
[10] M.Matloka, Sequences of fuzzy numbers, Busefal, 28(1986), 28-37.
[11] M.Mursaleen and M.Basarir, On some new sequence spaces of fuzzy numbers, Indian J. Pure Appl. Math., 34(9) (2003), 1351-1357.
[12] S.Nanda, On sequences of fuzzy numbers, Fuzzy Sets Syst. , 33(1989), 123-126.
[13] I.Niven and H.S.Zuckerman, An Introduction to the Theory of Numbers, fourth ed.,John Wiley and Sons, New York, 1980.
[14] F.Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Syst., 99(1998), 353-356.
[15] E.Savas, On strongly λ− summable sequences of fuzzy numbers, Inform. Sci., 125(2000), 181-186.
[16] I.J.Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(1959), 361-375.
[17] Congxin Wu and Guixiang Wang, Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application, Fuzzy Sets Syst., 130(2002), 383-390.
[18] L.A.Zadeh, Fuzzy sets, Inform Control, 8(1965), 338-353.
[19] H.Kizmaz, On certain sequence spaces, Canad Math. Bull. , 24(2)(1981), 169-176.
[20] M.Et and R.Colak, On some generalized difference sequence spaces, Soochow J. Math., 21(4)(1995), 377-386.
[21] M.Et, On some topological properties of generalized difference sequence spaces, Int. J. Math. Math. Sci., 24(11)(2000), 785-791.
[22] M.Et and F.Nuray, Δm− Statistical Convergence, Indian J. Pure Appl. Math., 32(6) (2001), 961-969.
[23] R.Colak, M.Et and E.Malkowsky, Some topics of sequence spaces, Lecture Notes in Mathematics, Firat University Press, Elazig, Turkey,2004.
[24] M.Isik, On statistical convergence of generalized difference sequences, Soochow J. Math., 30(2)(2004), 197-205.
[25] Y.Altin and M.Et, Generalized difference sequence spaces defined by a modulus function in a locally convex space, Soochow J. Math. , 31(2)(2005), 233-243.
[26] W.Orlicz, ¨Uber Raume LM Bull. Int. Acad. Polon. Sci. A, (1936), 93-107.
[27] J.Lindenstrauss and L.Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.
[28] S.D.Parashar and B.Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. , 25(4)(1994), 419-428.
[29] M.Mursaleen,M.A.Khan and Qamaruddin, Difference sequence spaces defined by Orlicz functions, Demonstratio Math. , Vol. XXXII (1999), 145-150.
[30] C.Bektas and Y.Altin, The sequence space M (p, q, s) on seminormed spaces, Indian J. Pure Appl. Math., 34(4) (2003), 529-534.
[31] B.C.Tripathy,M.Etand Y.Altin, Generalized difference sequence spaces defined by Orlicz function in a locally convex space, J. Analysis and Applications, 1(3)(2003), 175-192.
[32] K.Chandrasekhara Rao and N.Subramanian, The Orlicz space of entire sequences, Int. J. Math. Math. Sci., 68(2004), 3755-3764.
[33] M.A.Krasnoselskii and Y.B.Rutickii, Convex functions and Orlicz spaces, Gorningen, Netherlands, 1961.
[34] Nakano, Concave modulars, J. Math. Soc. Japan, 5(1953), 29-49.
[35] W.H.Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978.
[36] I.J.Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100(1) (1986), 161-166.
[37] H.I.Brown, The summability field of a perfect − method of summation, J. Anal. Math., 20(1967), 281-287.
[38] A.Wilansky, Summability through Functional Analysis, North-Holland Mathematical Studies, North-Holland Publishing, Amsterdam, Vol.85(1984).
[39] P.K.Kamthan and M.Gupta, Sequence spaces and series. Lecture Notes in Pure and Applied Mathematics, Marcel Dekker Inc. New York, 65(1981).
[40] P.K.Kamthan, Bases in a certain class of Frechet space, Tamkang J. Math., 1976, 41-49.
[41] C.Goffman and G.Pedrick, First Course in Functional Analysis, Prentice Hall India, New Delhi, 1974.