基于Orlicz函数及强Pre-Cauchy收敛的模糊数列空间
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摘要
作为统计收敛模糊数列空间的推广,基于Orlicz函数,在义模糊数列强Pre-Cauchy收敛的基础上,提出并研究模糊数列空间W(M,C, p)。同时,讨论模糊数列空间W(M,C, p)与统计Pre-Cauchy收敛的模糊数列空间S(C)之间的包含关系。
As an extension of the statistical convergent sequence space of fuzzy numbers,the sequence spaces of fuzzy numbers W(M,C,p) based on Orlicz functions and strongly Pre-Cauchy convergence are defined and discussed.In addition,the relationship between strongly Pre-Cauchy convergence and statistical Pre-Cauchy convergence.
As an extension of the statistical convergent sequence space of fuzzy numbers,the sequence spaces of fuzzy numbers W(M,C,p) based on Orlicz functions and strongly Pre-Cauchy convergence are defined and discussed.In addition,the relationship between strongly Pre-Cauchy convergence and statistical Pre-Cauchy convergence.
引文
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[17]冯雪.基于Orlicz函数的模糊数列几乎理想λ-统计收敛和强几乎理想λ-收敛[J].齐齐哈尔大学学报:自然科学版,2018,34(2):82-89
[18]NIVEN I.,ZUCKERMAN H.S..An Introduction to the Theory of Numbers[M].4th Ed.New York:John Willey and Sons,1980
[19]Sabiha Tabassum,Statistically Pre-Cauchy Triple Sequences and Orlicz Functions[J].Pure Mathematical Sciences,2018,7(01):1-9
[20]WU C.X.,WANG T.F..The Geometric Theory of Orlicz Spaces[M]Harbin:Harbin Institute Techonology Press,1986
[2]FRIDY J A.On statistical convergent[J].Analysis,1985,5(04):301-313
[3]FREEDMAN A R,SEMBER I J.Densities and summability[J].Pacific Journal of Mathematics,1981,95(02):293-305
[4]FRIDY J A,ORHAN C.Lacunary statistical convergence[J].Facific Journal of Mathematics,1993,160(01):43-51
[5]FRIDY J A,ORHAN C.Lacunary statistical summability[J].Journal of Mathematical Analysis and Applications,1993,173(02)497-504
[6]MURSALEEN M.λ-statistical convergence[J].Math.Slovaca,2000(50):111-115
[7]SAVAS E.On strong almost A-summability with respect to a modulus and statistical convergence[J].Indian J.Pure and Appl.Math.,1992,23(02):217-212
[8]L.A.Zzdeh.Fuzzy sets[J].Information and contral,1965(08):338-353
[9]M.Matloka.Sequences of fuzzy numbers[J].Busefal,1986,28:28-37
[10]SAVAS E.On statistically convergent sequences of fuzzy numbers[J].Information Sciences,2001,137(1-4):227-282
[11]AYTAR S,MAMMADOV M A,PEHLIVAN S.Statistical limit inferior and superior for sequence of fuzzy numbers[J].Fuzzy Set and Systems,2006,157(01):976-985
[12]LINDENSTRAUSS J.,TZAFRIRI L.On Orlicz sequence spaces[J].Israel J.Math.,1971,10(03):379-390
[13]PARASHAR S.D.,CHOUDHARY B..Sequence spaces defined by Orlicz functions[J].Indian J.Pure and Appl.Math.,1994,25(04)419-428
[14]MURSALEEN M.,KHAN Q.A..CHISHTI T.A.,Some new convergent sequences spaces defined by Orlicz functions and statistical convergence[J].Ital.J.Pure Appl.Math.,2001,9:25-32
[15]TRIPATHY B.C.,MAHANTA S..On a class of sequences related to the pl spaces defined by Orlicz function[J]Soochow J.Math.2003,29(04):379-391
[16]巩增泰,冯雪.基于Orlicz函数及强缺项收敛的模糊数列空间[J].陕西师范大学学报:自然科学版,2015,43(01):1-7.
[17]冯雪.基于Orlicz函数的模糊数列几乎理想λ-统计收敛和强几乎理想λ-收敛[J].齐齐哈尔大学学报:自然科学版,2018,34(2):82-89
[18]NIVEN I.,ZUCKERMAN H.S..An Introduction to the Theory of Numbers[M].4th Ed.New York:John Willey and Sons,1980
[19]Sabiha Tabassum,Statistically Pre-Cauchy Triple Sequences and Orlicz Functions[J].Pure Mathematical Sciences,2018,7(01):1-9
[20]WU C.X.,WANG T.F..The Geometric Theory of Orlicz Spaces[M]Harbin:Harbin Institute Techonology Press,1986