On fuzzy normed linear space valued statistically ∗ convergent sequences

  • Paritosh Chandra Das Rangia College.
Palabras clave: Convergence and divergence of series and sequences, Ideal and statistical convergence, Fuzzy set theory.

Resumen

In this article we define the notion of statistically convergent and statistically null sequences with the concept of fuzzy norm and discuss some of their properties such as completeness, monotone, solidness, symmetricity sequence algebra and convergence free.The work of the author is supported by University Grants Commission of India vide project No. F. 42-28/2013 (SR), dated 12 March, 2013, Rangia College, India.

Biografía del autor/a

Paritosh Chandra Das, Rangia College.
Department of Mathematics.

Citas

[1] N. R. Das, P. Das and A. Choudhury: Absolute value like fuzzy real number and fuzzy real-valued sequence spaces, Jour. Fuzzy Math., 4(2), pp. 421-433, (1996).

[2] A. Esi, : On some new paranormed sequence spaces of fuzzy numbers defined by Orlicz functions and statistical convergence, Math. Modell. Anal., 11(4), pp. 379-388, (2006).

[3] H. Fast: Sur la convergence statistique, Colloq. Math., 2, pp. 241-244, (1951).

[4] C. Felbin: Finit dimensional fuzzy normed linear space, Fu zzy Se ts Syst., 48, pp. 239-248, (1992).

[5] J. A. Fridy: On statistical convergence, Analysis, 5, pp. 301-313, (1985).

[6] O. Kelava and S. Seikkala: On fuzzy metric spaces, Fuzzy Se ts Sys t . , 12, pp. 215-229, (1984).

[7] S. Nanda: On sequences of fuzzy numbers, Fuzzy Set Syst., 33, pp. 123-126, (1989).

[8] F. Nuray and E. Savas: Statistical convergence of sequences of fuzzy real numbers, Math. Slovaca, 45 (3), pp. 269-273, (1995).

[9] T. Salat: On Statistically convergent sequences of real numbers, Math. Slovaca, 30 (2), pp. 139-150, (1980).

[10] E. Savas: A note on sequence of fuzzy numbers, Inf. Sci., 124, pp. 297-300, (2000).

[11] I. J. Schoenberg: The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, pp. 361-375, (1959).

[12] P. V. Subrahmanyam: Cesaro Summability for fuzzy real numbers;, J. Analysis, 7, pp. 159-168, (1999).

[13] Yu-R. Syau: Sequences in fuzzy metric space, Computers Math. Appl., 33(6), pp. 73-76, (1997).

[14] B. C. Tripathy: On generalized difference paranormed statistically convergent sequences, Indian J. Pure Appl. Math., 35(5), pp. 655-663, (2004).

[15] B. C. Tripathy and A. Baruah: Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50, pp. 565-574, (2010).

[16] B. C. Tripathy and A.J. Dutta: Bounded variation double sequence space of fuzzy real numbers, Comput. Math. Appl., 59 (2), pp. 1031- 1037, (2010).

[17] B. C. Tripathy and M. Sen: On generalized statistically convergent sequences, Indian J. Pure Appl. Math., 32(11), pp. 1689-1694, (2001).

[18] B. K. Tripathy and S. Nanda: Absolute value of fuzzy real numbers and fuzzy sequence spaces, Jour. Fuzzy Math., 8(4), pp. 883-892, (2000).
Publicado
2017-10-20
Cómo citar
Das, P. (2017). On fuzzy normed linear space valued statistically ∗ convergent sequences. Proyecciones. Journal of Mathematics, 36(3), 511-527. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2394
Sección
Artículos