Acta mathematica scientia, Series B >
SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS
Received date: 2007-03-27
Revised date: 2008-11-11
Online published: 2011-01-20
In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
Key words: Orlicz function; completeness; seminorm; regular convergence; solid space; symmetric space
Binod Chandra Tripathy , Bipul Sarma . SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 134 -140 . DOI: 10.1016/S0252-9602(11)60215-4
[1] Basarir M, Sonalcan O. On some double sequence spaces. J Indian Acad Math, 1999, 21(2)}: 193--200
[2] Bromwich T J Ia. An Introduction to the Theory of Infinite Series. New York: MacMillan and Co Ltd, 1965
[3] Hardy G H. On the convergence of certain multiple series. Proc Camb Phil Soc, 1917, 19: 86--95
[4] Kaleva O, Seikkala S. On fuzzy metric spaces. Fuzzy Sets and Systems, 1984, 12: 215--229
[5] Kamthan P K, Gupta M. Sequence Spaces and Series. Marcel Dekker, 1980
[6] Kizmaz H. On certain sequence spaces. Canad Math Bull, 1981, 24: 169--176
[7] Krasnoselkii M A, Rutitsky Y B. Convex Function and Orlicz Spaces. Groningen Netherlands, 1961
[8] Lindenstrauss J, Tzafriri L. On Orlicz sequence spaces. Israel J Math, 1971, 10: 379--390
[9] Matloka M. Sequences of fuzzy numbers. BUSEFAL, 1986, {\bf 28}: 28--37
[10] Moricz F. Extension of the spaces c and c0 from single to double sequences. Acta Math Hungerica, 1991, 57(1/2): 129--136
[11] Moricz F, Rhoades B E. Almost convergence of double sequences and strong regularity of summability matrices. Math Proc Camb Phil Soc, 1988, 104: 283--294
[12] Nakano H. Concave modulars. J Math Soc Japan, 1953, 5: 29--49
[13] Nanda S. On sequences of fuzzy numbers. Fuzzy Sets and Systems, 1989, 33: 123--126
[14] Nuray F. Lacunary statistical convergence of sequences of fuzzy numbers. Fuzzy Sets and Systems, 1998, 99: 353--356
[15] Nuray F, Savas E. Statistical convergence of fuzzy numbers. Math Slovaca, 1995, 45(3): 269--273
[16] Puri M L, Ralescu D A. Differentials of fuzzy functions. J Math Anal Appl, 1983, 91: 552--558
[17] Tripathy B C. Statistically convergent double sequences. Tamkang J Math, 2003, 34(3): 231--237
[18] Tripathy B C, Sarma B. Statistically convergent difference double sequence spaces. Acta Mathematica Sinica, 2008, 24(5): 737--742
[19] Tripathy B C, Sarma B. Vector valued double sequence spaces defined by Orlicz functions. Mathematica Slovaca, 2009, 59(6): 767--776
[20] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8: 338--353
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