Article http://dx.doi.org/10.26855/jamc.2020.12.016

Almost Convergence Property of Generalized Riesz Spaces


Abdul Hamid Ganie*, Dowlath Fathima

Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic Universtiy, Abha-M, Saudi Arabia.

*Corresponding author: Abdul Hamid Ganie

Published: December 23,2020


Quite recently, the sequence spacehas been study in Altay and Başar  and is given by

with  , . Also, the characterization of various matrix classes has been given. Also, the significant classes of almost convergent sequence have been studied in Lorentz. Jalal and Ganie have well structured this sequence space to the spaces of almost convergence and characterize some matrix classes concerning to this approach. We aim in this paper to introduce the new generalized sequence spacevia, of non-absolute type for s≥0. Some new type of topological properties will be structured. Furthermore, we also examine for characterizing the matrix classes of the form , where f , f   and f0  denote respectively the spaces of almost bounded sequences, almost convergent sequences and almost sequences converging to zero.


[1] Ganie, A. H. and Sheikh, N. A. (2013). On some new sequence space of non-absolute type and matrix transforma-tions, J. Egypt. Math. Soc., 21, 34-40.

[2] Neyaz, A. S. and Abdul, H. G. (2012). A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedagog. Nyiregyhaziensis, 28, 47-58.

[3] Banach, S. (1932). Theỏries des operations linẻaries, Warszawa.

[4] Sheikh, N. A., Jalal, T., and Ganie, A. H. (2013). New type of sequence spaces of non-absolute type and some ma-trix transformations, Acta Math. Acad. Paedagog. Nyiregyhaziensis, 29, 51-66. 

[5] Ganie, A. H. and Sheikh, N. A. (2015). Infinite matrices and almost convergence, Filomat, 29(6), 1183-1188.

[6] Ganie, A. H. and Antesar, A. (2020). Certain sequence spaces using ∆-operator, Adv. Stud. Contemp. Math. (Kyungshang), 30(1), 17-27.

[7] Lorentz, G. G. (1948). A contribution to the theory of divergent series, Acta Math., (80), 167-190.

[8] Abdul, H. G. (2020). Lacunary sequences with almost and statistical convergence, Annals Commu. Maths., 3(1), 46-53.

[9] Nanda, S. (1979). Matrix transformations and almost boundedness, Glasnik Mat., 14(34), 99-107.

[10] Abdul, H. G. (2020). Riesz spaces using modulus function, Int. jour. Math. Models & Methods in Appl. Sci., 14, 20-23. 

[11] Ganie, A. H., Mobin, A., Sheikh, N. A., and Jalal, T. (2016). New type of Riesz sequence space of non-absolute type, J. Appl. Comput. Math., 5(1), 1-4.

[12] Lascarides, C. G., Maddox, I. J. (1970). Matrix transformations between some classes of sequences, Proc. Camb. Phil. Soc., (68), 99-104.

[13] Sheikh, N. A. and Ganie, A. H. (2013). On the space of λ-convergent sequence and almost convergence, Thai J. Math., 2(11), 393-398.

[14] Altay, B. and Başar, F. (2002). On the paranormed reisz sequence space of non-absolute type, Southeast Asian Bulletin of Math., (26), 701-715.

[15] Ganie, A. H., Lone, S. A., and Akhter, A. (2020). Generalised Ceşaro difference sequence space of non-absolute type, EKSAKTA, 1(2), 147-153.

[16] Jalal, T. and Ganie, A. H. (2009). Almost convergence and some matrix transformation, International Jour. Math. (Shekhar New Series), 1(1), 133-138.

How to cite this paper

Almost Convergence Property of Generalized Riesz Spaces

How to cite this paper: Abdul Hamid Ganie, Dowlath Fathima. (2020) Almost Convergence Property of Generalized Riesz Spaces. Journal of Applied Mathematics and Computation, 4(4), 249-253.

DOI: http://dx.doi.org/10.26855/jamc.2020.12.016