Volume 19 • Issue 1 • PP: 68-81 • 2022
Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces
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© 2022 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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
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.
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