On Zweier I-convergent sequence spaces.

  • Vakeel A. Khan Aligarh Muslim University.
  • Khalid Ebadullah Aligarh Muslim University.
  • Yasmeen Aligarh Aligarh Muslim University.
Palabras clave: Ideal, filter, I-convergence field, monotone, solid, Lipschitz function, Zweier Space, statistical convergence, Banach space, filtro, campo de I-convergencia, monótono, sólido, función de Lipschitz, espacio de Zweier, convergencia estadística.

Resumen

In this article we introduce the Zweier I-convergent sequence spaces . We prove the decomposition theorem and study topo-logical, algebraic properties and have established some inclusion relations of these spaces.

Biografía del autor

Vakeel A. Khan, Aligarh Muslim University.
Department of Mathematics.
Khalid Ebadullah, Aligarh Muslim University.
Department of Applied Mathematics.
Yasmeen Aligarh, Aligarh Muslim University.
Department of Mathematics.

Citas

[1] Altay, B.,Basar, F. and Mursaleen. On the Euler sequence space which‏ include the spaces lp and l∞, Inform.Sci., 176 (10), pp. 1450-1462,‏ (2006).‏

[2] Basar, F. and Altay, B. On the spaces of sequences of p-bounded variation and related matrix mappings. Ukrainion Math. J. 55. (2003).‏

[3] Buck, R. C.: Generalized Asymptotic Density, Amer. J. Math. 75, pp.‏ 335-346, (1953).‏

[4] Connor, J. S.: it The statistical and strong P-Cesaro convergence of‏ sequences,Analysis. 8(1988),47-63.‏

[5] Connor, J. S. : On strong matrix summability with respect to a modulus‏ and statistical convergence, Cnad. Math. Bull. 32, pp. 194-198, (1989).‏

[6] Connor, J., Fridy, J. A. and Kline, J. Statistically Pre-Cauchy sequence,‏ Analysis. 14, pp. 311-317, (1994).‏

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

[8] Kamthan, P. K. and Gupta, M. : Sequence spaces and series. Marcel‏ Dekker Inc, New York.(1980).

[9] Khan, V. A. and Ebadullah, K. On some I-Convergent sequence spaces‏ defined by a modullus function. Theory and Application of Mathematiccs and Computer Science. 1 (2), pp. 22-30, (2011).‏

[10] Khan, V. A., Ebadullah, K and Ahmad, A. I-Pre-Cauchy Sequences‏ and Orlicz Function. Journal of Mathematical Analysis. 3 (1), pp. 21-26,‏ (2012).‏

[11] Khan, V.A. and Ebadullah,K.I-Convergent difference sequence spaces‏ defined by a sequence of moduli. J. Math. Comput.Sci. 2 (2), pp. 265-‏ 273, (2012).‏

[12] Kostyrko, P., Salat, T.,Wilczynski,W.I-convergence. Real Analysis Exchange, 26 (2), pp. 669-686, (2000).‏

[13] Malkowsky, E. Recent results in the theory of matrix transformation‏ in sequence spaces. Math. Vesnik. (49), pp. 187-196, (1997).‏

[14] Ng, P., N. and Lee P., Y. Cesaro sequence spaces of non-absolute type.‏ Comment. Math. Pracc. Math. 20 (2), pp. 429-433, (1978).‏

[15] Salat,T., Tripathy, B. C., Ziman, M. On some properties of Iconvergence. Tatra Mt. Math. Publ., (28), pp. 279-286, (2004).‏

[16] Salat, T., Tripathy, B. C.,Ziman,M. On I-convergence field. Ital. J.‏ Pure Appl. Math., (17), pp. 45-54 (2005).‏

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

[18] Sengönül, M. On The Zweier Sequence Space, DEMONSTRATIO‏ MATHEMATICA, Vol.XL No.(1), pp. 181-196, (2007).‏

[19] Tripathy, B. C. and Hazarika, B. Paranorm I-Convergent sequence‏ spaces, Math Slovaca. 59 (4), pp. 485-494. (2009).‏

[20] Tripathy, B. C. and Hazarika,B. Some I-Convergent sequence spaces‏ defined by Orlicz function., Acta Mathematicae Applicatae Sinica. 27‏ (1), pp 149-154, (2011).‏

[21] Tripathy, B. C. and Hazarika, B. I -convergent sequence spaces associated with multiplier sequence spaces ; Mathematical Inequalities and‏ Appl;ications ; 11 (3), pp. 543-548, (2008).

[22] Tripathy, B. C. and Mahanta, S. On Acceleration convergence of sequences ; Journal of the Franklin Institute, 347, pp. 591-598, (2010).‏

[23] Tripathy,B.C. and Hazarika, B. I-monotonic and I-Convergent sequences, Kyungpook Math. Journal. 51 (2) (2011), pp. 233-239, (2011).‏

[24] Tripathy, B. C. Sen, M. and Nath, S. I-Convergence in probabilistic‏ n-normed space ; Soft Comput, 16, pp. 1021-1027, (2012).‏

[25] Tripathy, B. C. Hazarika,B and Choudhry, B. Lacunary I-Convergent‏ sequences, Kyungpook Math. Journal. 52 (4), pp. 473-482, (2012).‏

[26] Tripathy, B. C. and Sharma, B. On I-Convergent double sequences of fuzzy real numbers, Kyungpook Math. Journal. 52 (2), pp. 189-200, (2012).

[27] Tripathy, B. C. and Ray, G. C. Mixed fuzzy ideal topological spaces ; Applied mathematics and Computaions; 220, pp. 602-607, (2013).
Publicado
2017-03-23
Cómo citar
Khan, V., Ebadullah, K., & Aligarh, Y. (2017). On Zweier I-convergent sequence spaces. Proyecciones. Journal of Mathematics, 33(3), 259-276. https://doi.org/10.4067/S0716-09172014000300003
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