Research Article
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The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function

Year 2016, Volume: 4 Issue: 3, 296 - 306, 30.09.2016

Deepmala Rai N. Subramanian Vishnu Narayan Mishra

https://izlik.org/JA73UT75RF

Abstract



In this article we introduce the sequence spaces





associated
with the integrated sequence space defined by Musielak. We study some basic
topological and algebraic properties of these spaces. We also investigate some
inclusion relations related to these spaces.




Keywords

Analytic sequence double sequences χ^2 space difference sequence space Musielak - Orlicz function p- metric space Ideal ideal convergent

References

  • T.J.I’A. Bromwich, An introduction to the theory of infinite series, Macmillan and Co.Ltd. ,New York, (1965).
  • G.H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917), 86-95.
  • F. Moricz, Extentions of the spaces c and c_0 from single to double sequences, Acta. Math. Hung., 57(1-2), (1991), 129-136.
  • F. Moricz and B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc., 104, (1988), 283-294.
  • M. Basarir and O. Solancan, On some double sequence spaces, J. Indian Acad. Math., 21(2) (1999), 193-200.
  • B.C. Tripathy, On statistically convergent double sequences, Tamkang J. Math., 34(3), (2003), 231-237.
  • A. Turkmenoglu, Matrix transformation between some classes of double sequences, J. Inst. Math. Comp. Sci. Math. Ser., 12(1), (1999), 23-31.
  • A. Go ̈khan and R. Colak, The double sequence spaces c_2^P (p) and c_2^PB (p), Appl. Math. Comput., 157(2), (2004), 491-501.
  • A. Go ̈khan and R. Colak, Double sequence spaces l_2^∞, ibid., 160(1), (2005), 147-153.
  • M. Zeltser, Investigation of Double Sequence Spaces by Soft and Hard Analitical Methods, Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1), (2003), 223-231.
  • B. Altay and F. Baaar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1), (2005), 70-90.
  • F. Başar and Y. Sever, The space L_p of double sequences, Math. J. Okayama Univ, 51, (2009), 149-157.
  • N. Subramanian and U.K. Misra, The semi normed space defined by a double gai sequence of modulus function, Fasciculi Math., 46, (2010).
  • I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100(1) (1986), 161-166.
  • J. Cannor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(2), (1989), 194-198.
  • A. Pringsheim, Zurtheorie derzweifach unendlichen zahlenfolgen, Math. Ann., 53, (1900), 289-321.
  • H.J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2, (1936), 29-60.
  • H.J. Hamilton, A Generalization of multiple sequences transformation, Duke Math. J., 4, (1938), 343-358.
  • H.J. Hamilton, Preservation of partial Limits in Multiple sequence transformations, Duke Math. J., 4, (1939), 293-297.
  • P.K. Kamthan and M. Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, In c., New York , 1981.
  • J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathematical Studies, North-Holland Publishing, Amsterdam, Vol.85(1984).
  • P. Kostyrko, T. Salat and W. Wilczynski, I- convergence, Real Anal. Exchange, 26(2) (2000-2001), 669-686, MR 2002e:54002.
  • V. Kumar and K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Inform. Sci., 178(24) (2008), 4670-4678.
  • V. Kumar, On I and I^*- convergence of double sequences, Mathematical communications, 12 (2007), 171-181.
  • B. Hazarika, On Fuzzy Real Valued I- Convergent Double Sequence Spaces, The Journal of Nonlinear Sciences and its Applications (in press).
  • B. Hazarika, On Fuzzy Real Valued I- Convergent Double Sequence Spaces defined by Musielak-Orlicz function, J. Intell. Fuzzy Systems, 25(1) (2013), 9-15, DOI: 10.3233/IFS-2012-0609.
  • B. Hazarika, Lacunary difference ideal convergent sequence spaces of fuzzy numbers, J. Intell. Fuzzy Systems, 25(1) (2013), 157-166, DOI: 10.3233/IFS-2012-0622.
  • B. Hazarika, On σ- uniform density and ideal convergent sequences of fuzzy real numbers, J. Intell. Fuzzy Systems, DOI: 10.3233/IFS-130769.
  • B. Hazarika, Fuzzy real valued lacunary I- convergent sequences, Applied Math. Letters, 25(3) (2012), 466-470.
  • B. Hazarika, Lacunary I- convergent sequence of fuzzy real numbers, The Pacific J. Sci. Techno., 10(2) (2009), 203-206.
  • B. Hazarika, On generalized difference ideal convergence in random 2-normed spaces, Filomat, 26(6) (2012), 1265-1274.
  • B. Hazarika, Some classes of ideal convergent difference sequence spaces of fuzzy numbers defined by Orlicz function, Fasciculi Mathematici, 52 (2014)(Accepted).
  • B. Hazarika, I- convergence and Summability in Topological Group, J. Informa. Math. Sci., 4(3) (2012), 269-283.
  • B. Hazarika, Classes of generalized difference ideal convergent sequence of fuzzy numbers, Annals of Fuzzy Math. and Inform., (in press).
  • B. Hazarika, On ideal convergent sequences in fuzzy normed linear spaces, Afrika Matematika, DOI: 10.1007/s13370-013-0168-0.
  • B. Hazarika and E. Savas, Some I- convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz functions, Math. Comp. Modell., 54(11-12) (2011), 2986-2998.
  • B. Hazarika,K. Tamang and B.K. Singh, Zweier Ideal Convergent Sequence Spaces Defined by Orlicz Function, The J. Math. and Computer Sci., (Accepted).
  • B. Hazarika and V.Kumar, Fuzzy real valued I- convergent double sequences in fuzzy normed spaces, J. Intell. Fuzzy Systems, (accepted).
  • B.C. Tripathy and B. Hazarika, I- convergent sequence spaces associated with multiplier sequences, Math. Ineq. Appl., 11(3) (2008), 543-548.
  • B.C. Tripathy and B. Hazarika, Paranorm I- convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
  • B.C. Tripathy and B. Hazarika, Some I- convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sinica, 27(1) (2011), 149-154.
  • B. Hazarika and A. Esi, On ideal convergent sequence spaces of fuzzy real numbers associated with multiplier sequences defined by sequence of Orlicz functions, Annals of Fuzzy Mathematics and Informatics, (in press).

Year 2016, Volume: 4 Issue: 3, 296 - 306, 30.09.2016

Deepmala Rai N. Subramanian Vishnu Narayan Mishra

https://izlik.org/JA73UT75RF

Abstract

References

  • T.J.I’A. Bromwich, An introduction to the theory of infinite series, Macmillan and Co.Ltd. ,New York, (1965).
  • G.H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917), 86-95.
  • F. Moricz, Extentions of the spaces c and c_0 from single to double sequences, Acta. Math. Hung., 57(1-2), (1991), 129-136.
  • F. Moricz and B.E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc., 104, (1988), 283-294.
  • M. Basarir and O. Solancan, On some double sequence spaces, J. Indian Acad. Math., 21(2) (1999), 193-200.
  • B.C. Tripathy, On statistically convergent double sequences, Tamkang J. Math., 34(3), (2003), 231-237.
  • A. Turkmenoglu, Matrix transformation between some classes of double sequences, J. Inst. Math. Comp. Sci. Math. Ser., 12(1), (1999), 23-31.
  • A. Go ̈khan and R. Colak, The double sequence spaces c_2^P (p) and c_2^PB (p), Appl. Math. Comput., 157(2), (2004), 491-501.
  • A. Go ̈khan and R. Colak, Double sequence spaces l_2^∞, ibid., 160(1), (2005), 147-153.
  • M. Zeltser, Investigation of Double Sequence Spaces by Soft and Hard Analitical Methods, Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1), (2003), 223-231.
  • B. Altay and F. Baaar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1), (2005), 70-90.
  • F. Başar and Y. Sever, The space L_p of double sequences, Math. J. Okayama Univ, 51, (2009), 149-157.
  • N. Subramanian and U.K. Misra, The semi normed space defined by a double gai sequence of modulus function, Fasciculi Math., 46, (2010).
  • I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100(1) (1986), 161-166.
  • J. Cannor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(2), (1989), 194-198.
  • A. Pringsheim, Zurtheorie derzweifach unendlichen zahlenfolgen, Math. Ann., 53, (1900), 289-321.
  • H.J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2, (1936), 29-60.
  • H.J. Hamilton, A Generalization of multiple sequences transformation, Duke Math. J., 4, (1938), 343-358.
  • H.J. Hamilton, Preservation of partial Limits in Multiple sequence transformations, Duke Math. J., 4, (1939), 293-297.
  • P.K. Kamthan and M. Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, In c., New York , 1981.
  • J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathematical Studies, North-Holland Publishing, Amsterdam, Vol.85(1984).
  • P. Kostyrko, T. Salat and W. Wilczynski, I- convergence, Real Anal. Exchange, 26(2) (2000-2001), 669-686, MR 2002e:54002.
  • V. Kumar and K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Inform. Sci., 178(24) (2008), 4670-4678.
  • V. Kumar, On I and I^*- convergence of double sequences, Mathematical communications, 12 (2007), 171-181.
  • B. Hazarika, On Fuzzy Real Valued I- Convergent Double Sequence Spaces, The Journal of Nonlinear Sciences and its Applications (in press).
  • B. Hazarika, On Fuzzy Real Valued I- Convergent Double Sequence Spaces defined by Musielak-Orlicz function, J. Intell. Fuzzy Systems, 25(1) (2013), 9-15, DOI: 10.3233/IFS-2012-0609.
  • B. Hazarika, Lacunary difference ideal convergent sequence spaces of fuzzy numbers, J. Intell. Fuzzy Systems, 25(1) (2013), 157-166, DOI: 10.3233/IFS-2012-0622.
  • B. Hazarika, On σ- uniform density and ideal convergent sequences of fuzzy real numbers, J. Intell. Fuzzy Systems, DOI: 10.3233/IFS-130769.
  • B. Hazarika, Fuzzy real valued lacunary I- convergent sequences, Applied Math. Letters, 25(3) (2012), 466-470.
  • B. Hazarika, Lacunary I- convergent sequence of fuzzy real numbers, The Pacific J. Sci. Techno., 10(2) (2009), 203-206.
  • B. Hazarika, On generalized difference ideal convergence in random 2-normed spaces, Filomat, 26(6) (2012), 1265-1274.
  • B. Hazarika, Some classes of ideal convergent difference sequence spaces of fuzzy numbers defined by Orlicz function, Fasciculi Mathematici, 52 (2014)(Accepted).
  • B. Hazarika, I- convergence and Summability in Topological Group, J. Informa. Math. Sci., 4(3) (2012), 269-283.
  • B. Hazarika, Classes of generalized difference ideal convergent sequence of fuzzy numbers, Annals of Fuzzy Math. and Inform., (in press).
  • B. Hazarika, On ideal convergent sequences in fuzzy normed linear spaces, Afrika Matematika, DOI: 10.1007/s13370-013-0168-0.
  • B. Hazarika and E. Savas, Some I- convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz functions, Math. Comp. Modell., 54(11-12) (2011), 2986-2998.
  • B. Hazarika,K. Tamang and B.K. Singh, Zweier Ideal Convergent Sequence Spaces Defined by Orlicz Function, The J. Math. and Computer Sci., (Accepted).
  • B. Hazarika and V.Kumar, Fuzzy real valued I- convergent double sequences in fuzzy normed spaces, J. Intell. Fuzzy Systems, (accepted).
  • B.C. Tripathy and B. Hazarika, I- convergent sequence spaces associated with multiplier sequences, Math. Ineq. Appl., 11(3) (2008), 543-548.
  • B.C. Tripathy and B. Hazarika, Paranorm I- convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
  • B.C. Tripathy and B. Hazarika, Some I- convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sinica, 27(1) (2011), 149-154.
  • B. Hazarika and A. Esi, On ideal convergent sequence spaces of fuzzy real numbers associated with multiplier sequences defined by sequence of Orlicz functions, Annals of Fuzzy Mathematics and Informatics, (in press).
There are 44 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Deepmala Rai This is me

N. Subramanian This is me

Vishnu Narayan Mishra This is me

Publication Date September 30, 2016
IZ https://izlik.org/JA73UT75RF
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Rai, D., Subramanian, N., & Narayan Mishra, V. (2016). The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function. New Trends in Mathematical Sciences, 4(3), 296-306. https://izlik.org/JA73UT75RF
AMA 1.Rai D, Subramanian N, Narayan Mishra V. The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function. New Trends in Mathematical Sciences. 2016;4(3):296-306. https://izlik.org/JA73UT75RF
Chicago Rai, Deepmala, N. Subramanian, and Vishnu Narayan Mishra. 2016. “The Generalized Difference of ∫ χ^2I of Fuzzy Real Numbers over P- Metric Spaces Defined by Musielak Orlicz Function”. New Trends in Mathematical Sciences 4 (3): 296-306. https://izlik.org/JA73UT75RF.
EndNote Rai D, Subramanian N, Narayan Mishra V (September 1, 2016) The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function. New Trends in Mathematical Sciences 4 3 296–306.
IEEE [1]D. Rai, N. Subramanian, and V. Narayan Mishra, “The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 296–306, Sept. 2016, [Online]. Available: https://izlik.org/JA73UT75RF
ISNAD Rai, Deepmala - Subramanian, N. - Narayan Mishra, Vishnu. “The Generalized Difference of ∫ χ^2I of Fuzzy Real Numbers over P- Metric Spaces Defined by Musielak Orlicz Function”. New Trends in Mathematical Sciences 4/3 (September 1, 2016): 296-306. https://izlik.org/JA73UT75RF.
JAMA 1.Rai D, Subramanian N, Narayan Mishra V. The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function. New Trends in Mathematical Sciences. 2016;4:296–306.
MLA Rai, Deepmala, et al. “The Generalized Difference of ∫ χ^2I of Fuzzy Real Numbers over P- Metric Spaces Defined by Musielak Orlicz Function”. New Trends in Mathematical Sciences, vol. 4, no. 3, Sept. 2016, pp. 296-0, https://izlik.org/JA73UT75RF.
Vancouver 1.Rai D, Subramanian N, Narayan Mishra V. The Generalized difference of ∫ χ^2I of fuzzy real numbers over p- metric spaces defined by Musielak Orlicz function. New Trends in Mathematical Sciences [Internet]. 2016 Sept. 1;4(3):296-30. Available from: https://izlik.org/JA73UT75RF