Some geometric properties of lacunary Zweier Sequence Spaces of order a.
DOI:
https://doi.org/10.4067/S0716-09172016000400009Keywords:
Lacunary sequence, Zweier operator, order continuous, Fatou property, Banach-Saks property, secuencia lagunar, operador de ZweierAbstract
In this paper we introduce a new sequence space using Zweier matrix operator and lacunary sequence of order a. Also we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space.References
[1] R. Colak, C. A. Bektas A-statistical convergence of order a, Acta Math. Sci., 31 (3), pp. 953-959, (2011).
[2] R. Colak, Statistical Convergence of Order a, Modern Methods in Analysis and Its Applications, pp. 121-129. Anamaya Pub., New Delhi (2010).
[3] Y. A. Cui, H. Hudzik, On the Banach-Saks and weak Banach-Saks properties of some Bannach sequence spaces, Acta Sci. Math.(Szeged), 65, pp. 179-187, (1999).
[4] J. Diestel, Sequence and Series in Banach spaces, in Graduate Texts in Math., Vol. 92, Springer-Verlag, (1984).
[5] A. Esi, A. Sapszoglu, On some lacunary a-strong Zweier convergent sequence spaces, Romai J., 8 (2), pp. 61-70, (2012).
[6] M. Et, M. Cinar, M. Karaka¸ s, On A-statistical convergence of order a of sequences of function, J. Inequa. Appl., 2013:204, (2013).
[7] M. Et, S. A. Mohiuddine, A. Alotaibi, On A-statistical convergence and strongly A-summable functions of order a, J. Inequa. Appl., 2013:469, (2013).
[8] M. Et, V. Karakaya, A new difference sequence set of order a and its geometrical properties, Abst. Appl. Anal., Volume 2014, Article ID 278907, 4 pages, (2014).
[9] M. Et, M. Karakas, Muhammed Cinar, Some geometric properties of a new modular space defined by Zweier operator, Fixed point Theory Appl., 2013:165, (2013).
[10] B. Hazarika, K. Tamang, B. K. Singh, Zweier ideal convergent sequence spaces defined by Orlicz function, The J. Math. Comp. Sci., 8 (3), pp. 307-318, (2014).
[11] B. Hazarika, K. Tamang, B. K. Singh, On paranormed Zweier ideal convergent sequence spaces defined by Orlicz Function, J. Egypt. Math. Soc., 22 (3), pp. 413-419, (2014).
[12] Y. F. Karababa and A. Esi, On some strong Zweier convergent sequence spaces, Acta Univ. Apulensis, 29, pp. 9-15, (2012).
[13] M. Karakas, M. Et, V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math. Ser. B. Engl. Ed., 33 (6), pp. 1711-1720, (2013).
[14] V. A. Khan, K. Ebadullah, A. Esi, N. Khan, M. Shafiq, On Paranorm Zweier I-convergent sequences spaces, Inter. J. Anal., Vol. 2013, Article ID 613501, 6 pages, (2013).
[15] V. A. Khan, K. Ebadullah, A. Esi, M. Shafiq, On some Zweier Iconvergent sequence spaces defined by a modulus function, Afr. Mat. DOI 10.1007/s13370-013-0186-y (2013).
[16] V. A. Khan, A. H. Saifi, Some geometric properties of a generalized Cesáro Masielak-Orlicz sequence space, Thai J. Math., 1 (2), pp. 97-108, (2003).
[17] V. A. Khan, Some geometric properties for N¨ orlund sequence spaces, Nonlinear Anal. Forum, 11(1), pp. 101-108, (2006).
[18] V. A. Khan, Some geometric properties of a generalized Ces´ aro sequence space, Acta Math. Univ. Comenian, 79 (1), pp. 1-8, (2010).
[19] V. A. Khan, Some geometrical properties of Riesz-Musielak-Orlicz sequence spaces, Thai J. Math., 8(3), pp. 565-574, (2010).
[20] V. A. Khan, Some geometrical properties of generalized lacunary strongly convergent sequence space, J. Math. Anal., 2(2), pp. 6-14, (2011).
[21] L. Leindler, Uber die la Vallee-Pousinsche Summierbarkeit Allgemeiner Orthogonalreihen. Acta Math. Acad. Sci. Hung., 16, pp. 375-387, (1965).
[22] M. Mursaleen, R. Colak, M. Et, Some geometric inequalities in a new Banach sequence space, J. Ineq. Appl., Article ID 86757, 6, (2007).
[23] M. Mursaleen, V. A. Khan, Some geometric properties of a sequence space of Riesz mean, Thai J. Math., 2, pp. 165-171, (2004).
[24] M. Sëngonül, On the Zweier sequence space, Demonstratio Math. Vol.XL No. (1), pp. 181-196, (2007).
[25] A. Wilansky, Summability Theory and its Applications, North-Holland Mathematics Studies 85, Elsevier Science Publications, Amsterdam, New York: Oxford, (1984).
[2] R. Colak, Statistical Convergence of Order a, Modern Methods in Analysis and Its Applications, pp. 121-129. Anamaya Pub., New Delhi (2010).
[3] Y. A. Cui, H. Hudzik, On the Banach-Saks and weak Banach-Saks properties of some Bannach sequence spaces, Acta Sci. Math.(Szeged), 65, pp. 179-187, (1999).
[4] J. Diestel, Sequence and Series in Banach spaces, in Graduate Texts in Math., Vol. 92, Springer-Verlag, (1984).
[5] A. Esi, A. Sapszoglu, On some lacunary a-strong Zweier convergent sequence spaces, Romai J., 8 (2), pp. 61-70, (2012).
[6] M. Et, M. Cinar, M. Karaka¸ s, On A-statistical convergence of order a of sequences of function, J. Inequa. Appl., 2013:204, (2013).
[7] M. Et, S. A. Mohiuddine, A. Alotaibi, On A-statistical convergence and strongly A-summable functions of order a, J. Inequa. Appl., 2013:469, (2013).
[8] M. Et, V. Karakaya, A new difference sequence set of order a and its geometrical properties, Abst. Appl. Anal., Volume 2014, Article ID 278907, 4 pages, (2014).
[9] M. Et, M. Karakas, Muhammed Cinar, Some geometric properties of a new modular space defined by Zweier operator, Fixed point Theory Appl., 2013:165, (2013).
[10] B. Hazarika, K. Tamang, B. K. Singh, Zweier ideal convergent sequence spaces defined by Orlicz function, The J. Math. Comp. Sci., 8 (3), pp. 307-318, (2014).
[11] B. Hazarika, K. Tamang, B. K. Singh, On paranormed Zweier ideal convergent sequence spaces defined by Orlicz Function, J. Egypt. Math. Soc., 22 (3), pp. 413-419, (2014).
[12] Y. F. Karababa and A. Esi, On some strong Zweier convergent sequence spaces, Acta Univ. Apulensis, 29, pp. 9-15, (2012).
[13] M. Karakas, M. Et, V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math. Ser. B. Engl. Ed., 33 (6), pp. 1711-1720, (2013).
[14] V. A. Khan, K. Ebadullah, A. Esi, N. Khan, M. Shafiq, On Paranorm Zweier I-convergent sequences spaces, Inter. J. Anal., Vol. 2013, Article ID 613501, 6 pages, (2013).
[15] V. A. Khan, K. Ebadullah, A. Esi, M. Shafiq, On some Zweier Iconvergent sequence spaces defined by a modulus function, Afr. Mat. DOI 10.1007/s13370-013-0186-y (2013).
[16] V. A. Khan, A. H. Saifi, Some geometric properties of a generalized Cesáro Masielak-Orlicz sequence space, Thai J. Math., 1 (2), pp. 97-108, (2003).
[17] V. A. Khan, Some geometric properties for N¨ orlund sequence spaces, Nonlinear Anal. Forum, 11(1), pp. 101-108, (2006).
[18] V. A. Khan, Some geometric properties of a generalized Ces´ aro sequence space, Acta Math. Univ. Comenian, 79 (1), pp. 1-8, (2010).
[19] V. A. Khan, Some geometrical properties of Riesz-Musielak-Orlicz sequence spaces, Thai J. Math., 8(3), pp. 565-574, (2010).
[20] V. A. Khan, Some geometrical properties of generalized lacunary strongly convergent sequence space, J. Math. Anal., 2(2), pp. 6-14, (2011).
[21] L. Leindler, Uber die la Vallee-Pousinsche Summierbarkeit Allgemeiner Orthogonalreihen. Acta Math. Acad. Sci. Hung., 16, pp. 375-387, (1965).
[22] M. Mursaleen, R. Colak, M. Et, Some geometric inequalities in a new Banach sequence space, J. Ineq. Appl., Article ID 86757, 6, (2007).
[23] M. Mursaleen, V. A. Khan, Some geometric properties of a sequence space of Riesz mean, Thai J. Math., 2, pp. 165-171, (2004).
[24] M. Sëngonül, On the Zweier sequence space, Demonstratio Math. Vol.XL No. (1), pp. 181-196, (2007).
[25] A. Wilansky, Summability Theory and its Applications, North-Holland Mathematics Studies 85, Elsevier Science Publications, Amsterdam, New York: Oxford, (1984).
Published
2017-03-23
How to Cite
[1]
K. Tamang and B. Hazarika, “Some geometric properties of lacunary Zweier Sequence Spaces of order a.”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 481-490, Mar. 2017.
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