On some new scenario of \(\Delta\)-spaces

Volume 14, Issue 3, pp 163--167 http://dx.doi.org/10.22436/jnsa.014.03.05

Publication Date: November 19, 2020 Submission Date: September 15, 2020 Revision Date: September 30, 2020 Accteptance Date: October 22, 2020

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1016 Downloads
• 1843 Views

Authors

Dowlath Fathema - Basic Science Department, College of Science and Theoretical Studies- Abha-F, Saudi Electronic University, KSA. Abdul Hamid Ganie - Basic Science Department, College of Science and Theoretical Studies- Abha-M, Saudi Electronic University, KSA.

Abstract

The structure of the Cesáro spaces were investigated by various authors as cited in the text. The scenario of this manuscript is to bring out the spaces \(\mathfrak{C}_{1}\left(\triangle^s_g\right)\) and \(\mathfrak{C}_{\infty}\left[\triangle^s_g\right]\) of Cesáro type for \(s\in \mathbb{N}=\{0,1,2,\ldots \}\). We will study some of their basic topological properties and obtain some inclusion relations concerning these spaces.

Share and Cite

Keywords

• Cesáro sequence space
• difference operator
• \(BK\)-space

MSC

•  40A05
•  46A45

References

• [1] M. Başarır, Paranormed Cesaro difference sequence space and related matrix transformations, Turk. J. Math., 15 (1991), 14--19
  • View Article
  • Google Scholar


• [2] Ç. A. Bektaş, M. Et, R. Çolak, Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292 (2004), 423--432
  • View Article
  • Google Scholar


• [3] V. K. Bhardwaj, S. P. Gupta, R. Karan, Köthe-Toeplitz duals and matrix transformations of Cesaro difference sequence spaces of second order, J. Math. Anal., 5 (2014), 1--11
  • View Article
  • Google Scholar


• [4] R. G. Cooke, Infinite matrices and sequence spaces, Macmillan & Co., London (1950)
  • View Article
  • Google Scholar


• [5] M. Et, On some generalised Ces`aro difference sequence spaces, Istanb. Univ. Sci. Fac. J. Math. Phys. Astronom, 55 (1997), 221--229
  • Google Scholar


• [6] A. R. Freedman, J. J. Sember, M. Raphael, Some Cesàro‐Type Summability Spaces, Proc. London Math. Soc., 37 (1978), 508--520
  • View Article
  • Google Scholar


• [7] A. H. Ganie, M. Ahmad, N. A. Sheikh, T. Jalal, New type of Riesz sequence space of non-absolute type, J. Appl. Computat. Math., 5 (2016), 1--4
  • View Article
  • Google Scholar


• [8] A. H. Ganie, A. Aldawoud, Certain sequence spaces using Delta-operator, Adv. Stud. Contemp. Math., 30 (2020), 17--27
  • View Article


• [9] A. H. Ganie, S. A. Lone, A. Akhter, Generalised difference sequence space of non- absolute type, EKSAKTA, 1 (2020), 147--153
  • View Article
  • Google Scholar


• [10] A. H. Ganie, N. A. Sheikh, On some new sequence space of non-absolute type and matrix transformations, J. Egyptian Math. Soc., 21 (2013), 108--114
  • View Article
  • Google Scholar


• [11] A. H. Ganie, N. A. Sheikh, Generalized difference sequence spaces of Fuzzy numbers, New York J. Math., 19 (2013), 431--438
  • View Article
  • Google Scholar


• [12] A. H. Ganie, N. A. Sheikh, Infinite matrices and almost convergence, Filomat, 29 (2015), 1183--1188
  • View Article
  • Google Scholar


• [13] A. H. Ganie, S. A. Gupkari, A. Akhter, Invariant means of sequences with statistical behaviour, Int. J. Cre. Res. Thoug., 8 (2020), 2702--2705
  • View Article


• [14] A. A. Jagers, A note on Cesaro sequence spaces, Nieuw Arch. Wisk.,, 22 (1974), 113--124
  • Google Scholar


• [15] H. Kizmaz, On certain sequences, Canad. Math. Bull., 24 (1981), 169--176
  • View Article


• [16] M. Mursaleen, A. H. Ganie, N. A. Sheikh, New type of generalized difference sequence space of non-absolute type and some matrix transformations, Filomat, 28 (2014), 1381--1392
  • View Article
  • Google Scholar


• [17] P.-N. Ng, P.-Y. Lee, Cesaro sequences spaces of non-absolute type, Comment Math. Prace Math., 20 (1978), 429--433
  • View Article


• [18] C. Orhan, Cesaro difference sequence spaces related matrix transformations, Comm. Fac. Sci. Univ. Ankara Ser. A1 Math., 32 (1983), 55--63
  • View Article


• [19] N. A. Sheikh, A. H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedagog. Nyhazi., 28 (2012), 47--58
  • View Article
  • Google Scholar


• [20] N. A. Sheikh, A. H. Ganie, A new type of sequence space of non-absolute type and matrix transformation, WSEAS Trans. J. Math., 12 (2013), 852--859
  • View Article
  • Google Scholar


• [21] N. A. Sheikh, T. Jalal, A. H. Ganie, New type of sequence spaces of non-absolute type and some matrix transformations, Acta Math. Acad. Paedagog. Nyhazi., 29 (2013), 51--66
  • View Article
  • Google Scholar


• [22] J.-S. Shiue, On the Cesaro sequence spaces, Tamkang J. Math, 1 (1970), 19--25
  • Google Scholar


• [23] B. C. Tripathy, A. Esi, A new type of difference sequence spaces, Int. J. Sci. Technol., 1 (2006), 11--14
  • View Article
  • Google Scholar


• [24] B. C. Tripathy, A. Esi, B. K. Tripathy, On new types of generalized difference Cesaro sequence spaces, Soochow J. Math., 31 (2005), 333--340
  • View Article
  • Google Scholar