International Journal of Neutrosophic Science

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Volume 19 , Issue 1 , PP: 68-81, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces

Archana Sharma 1 * , Sajid Murtaza 2 , Vijay Kumar 3

  • 1 Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India - (dr.archanasharma1022@gmail.com)
  • 2 Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India - (sajidsulimani8@gmail.com)
  • 3 Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India - (kaushikvjy@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190105

    Received: March 26, 2022 Accepted: September 04, 2022
    Abstract

    In the present paper, we use the difference operator ∆m (Iλ )-summability to define some new summability concepts on neutrosophic normed spaces. We also introduce concepts of generalized limit point, and cluster point and obtain some relationships among these notions. Finally, we define generalized Cauchy sequences on these spaces and present a characterization of a new summability method that preserves linear operators on neutrosophic normed spaces.

    Keywords :

    Neutrosophic normed spaces , lacunary convergence , and I-convergence.

    References

    [1] K Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87–96.

    [2] T. Bera and N.K. Mahapatra, Neutrosophic soft linear spaces, Fuzzy Information and

    Engineering, 9 (2017), 299–324.

    [3] T. Bera and N.K. Mahapatra, Neutrosophic soft normed linear spaces, Neutrosophic Sets and

    Systems, 23 (2018), 52–71.

    [4] B. Choudhary, Lacunary I-convergent sequences, Real Analysis Exchange, Summer

    Symposium, 2009, 56–57.

    [5] J. S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988),

    47–63.

    [6] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Computers

    and Mathematics with Applications, 63 (2012), 708–715.

    [7] K. Demirci, -limit superior and inferior, Math. Commun., 6(2001), 165 - 172.

    [8] K. Dems, On I-Cauchy sequences, Real Analysis Exchange, 30(2004), 123 -128.

    [9] H. Fast, Surla convergence statistique, Coll. Math., 2 (1951), 241–244.

    [10] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.

    [11] J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43–51.

    [12] B. Hazarika, V. Kumar and B. Lafuerza-Guillén, Generalized ideal convergence in Intuitionistic

    fuzzy normed linear spaces, Filomat, 27 (5), 811-820.

    [13] Soheyb Milles , Abdelkrim Latrech , Omar Barkat. (2020). Completeness and Compactness in

    Standard Single Valued Neutrosophic Metric Spaces, International Journal of Neutrosophic

    Science, Vol. 12(2): 96-104

    [14] M. Kirisci and Simsek, Neutrosophic normed spaces and statistical convergence, The Journal of

    Analysis, 28(2020), 1059-1073.

    [15] A. Komisarski, Pointwise -convergence and *-convergence in measure of sequences of

    functions, J. Math. Anal. Appl., 340 (2008), 770–779.

    [16] P. Kostyrko, T. Salat, W. Wilczynski, convergence, Real Anal. Exchange, 26(2) (2000/2001),

    669–686.

    [17] P. Kostyrko, M. Macaj, T. Salat and, M. Sleziak, -convergence and extremal -limit points,

    Math. Slovaca, 4(2005), 443 - 464.

    [18] V. Kumar, On and *-convergence of double sequences, Math. Commun, 12 (2007), 171–181,

    [19] V. Kumar and B. Lafuerza-Guillén, On ideal convergence of double sequences in probabilistic

    normed spaces, Acta Mathematica Sinica, 29(2012), 1689-1700.

    [20] LEINDLER, L.: Uber die de la Vallee-Pousinsche Summierbarkeit allgemeiner

    Orthogonalreihen, Acta Math. Acad. Sci. Hungar. 16 (1965), 375-387

    [21] M. Mursaleen, S. A. Mohiuddine, and O.H.H. Edley, On ideal convergence of double sequences

    in Intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603-611.

    [22] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039–46.

    [23] R Saadati, J H Park. On the Intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals,

    27(2006), 331–44.

    [24] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139–

    150.

    [25] I. J. Schoenberg, The inerrability of certain functions and related summability methods, Amer.

    Math. Monthly, 66 (1959), 361–375.

    [26] B. Schweizer, A. Sklar, Statistical metric spaces. Pacific J Math 10(1960), 314–44.

    [27] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, International

    Journal of Pure and Applied Mathematics, 24(2005), 287–297.

    [28] LA. Zadeh Fuzzy sets, Inform Control, 8(1965), 338–353.

    Cite This Article As :
    Sharma, Archana. , Murtaza, Sajid. , Kumar, Vijay. Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 68-81. DOI: https://doi.org/10.54216/IJNS.190105
    Sharma, A. Murtaza, S. Kumar, V. (2022). Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science, (), 68-81. DOI: https://doi.org/10.54216/IJNS.190105
    Sharma, Archana. Murtaza, Sajid. Kumar, Vijay. Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science , no. (2022): 68-81. DOI: https://doi.org/10.54216/IJNS.190105
    Sharma, A. , Murtaza, S. , Kumar, V. (2022) . Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science , () , 68-81 . DOI: https://doi.org/10.54216/IJNS.190105
    Sharma A. , Murtaza S. , Kumar V. [2022]. Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science. (): 68-81. DOI: https://doi.org/10.54216/IJNS.190105
    Sharma, A. Murtaza, S. Kumar, V. "Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces," International Journal of Neutrosophic Science, vol. , no. , pp. 68-81, 2022. DOI: https://doi.org/10.54216/IJNS.190105