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

Full Length Article

•

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

DOI

format_quote Cite this article

View PDF open_in_new

Abstract

In present paper we use the difference operator ∆^m and λ-summability to define the new concepts of ∆^m (λ)-convergence and ∆^m (I_λ)-convergence on neutrosophic normed spaces (briefly known as NNS). We also introduce concepts of ∆^m (I_λ)-limit point, ∆^m (I_λ)-cluster point and obtain some relationships among these notions. Finally, we define ∆^m (λ)-Cauchy, 〖∆^m (I〗_λ)-Cauchy sequences on these spaces and present a characterization for ∆^m (I_λ)-convergence preserving linear operators on neutrosophic normed spaces

Keywords

Neutrosophic normed spaces lacunary convergence and I-convergence.

References

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] M. Kirisci, and N. Simsek., Neutrosophic metric spaces, arXiv:1907.00798.

[14] M. Kirisci and Simsek, Neutrosophic normed spaces and statistical convergence, The Journal of Analysis, https://doi.org/10.1007/s41478-020-00234-0

[15] A. Komisarski, Point wise -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. Edely, 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

Choose your preferred format

format_quote

. "Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces." International Journal of Neutrosophic Science, vol. , no. , , pp. . DOI:

(). Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science, (), . DOI:

. "Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces." International Journal of Neutrosophic Science , no. (): . DOI:

() 'Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces', International Journal of Neutrosophic Science, (), pp. . DOI:

. Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces. International Journal of Neutrosophic Science. ;():. DOI:

, "Some remarks on ∆^m (I_λ )-summability on neutrosophic normed spaces," International Journal of Neutrosophic Science, vol. , no. , pp. , . DOI:

Digital Archive Ready