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On Some Properties of Difference Operator with Some Characterizations

Open Access
|Nov 2022

References

  1. [1] BAS¸AR, F.—ALTAY, B.: On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (2003), no. 1, 136–147.
  2. [2]ÇOLAK, R.—ET, M.: On some generalized difference sequence spaces and related matrix transformations, Hokkaido Math. J. 26(1997), no. 3, 483–492.
  3. [3] FATHIMA, D.—GANIE, A. H.: On some new scenario of Δ-spaces, J. Nonlinear Sci. Appl. 14 (2021), 163–167.10.22436/jnsa.014.03.05
  4. [4] FATHIMA, D.—M ALBAIDANI, M.—GANIE, A. H—AKHTER, A.: New structure of Fibonacci numbers using concept of Δ-operator, J. Math. Comput. Sci. 26 (2022), no. 2, 101–112.
  5. [5] GANIE, A. H: Sequences of Cesàro type using Lacunary notion,Int.Journal Nonlinear Anal. Appl. 2022 Paper: ID IJNAA-2008-2242(R1), 7 pp. http://dx.doi.org/10.22075/ijnaa.2021.21237.2242
  6. [6] GANIE, A. H—ANTESAR, A.: Certain spaces using Δ-operator, Adv. Stud. Contemp. Math. (Kyungshang) 30 (2020), no. 1, 17–27.
  7. [7] GANIE, A. H—SHEIKH, N. A.: On some new sequence space of non-absolute type and matrix transformations, J. Egyptain Math. Soc. 21( 2013), 34–40.10.1016/j.joems.2013.01.006
  8. [8] GANIE, A. H—SHEIKH, N. A.: Infinite matrices and almost convergence, Filomat, 29 (2015), no. (6), 1183–1188.
  9. [9] GANIE, A. H.—TRIPATHY, B. C.—SHEIKH, N. A.—SEN, M.: Invariant means and matrix transformations, Functional Analysis: Theory, Methods and Appl. 2 (2016), 28–33. http://vonneumann-publishing.com/fatma/articles-50-invariant-means-and-matrix-ransformations
  10. [10] DE MALAFOSSE, B.—MALKOWSKY, E.: On the measure of noncompactness of linear operators in spaces of strongly α-summable and bounded sequences,Period. Math. Hungar. 55 (2007), no. 2, 129–148.
  11. [11] DE MALAFOSSE, B.—V. RAKOČEVIĆ, V.: Applications of mesure of noncompactness in operators on the spaces sα,sα0, sα(c) ℓα(p), J. Math. Anal. Appl. 323 (2006), no. 1, 131–145.
  12. [12] DJOLOVIĆ, I.: Compact operators on the spaces a0r (Δ) and acr (Δ), J. Math. Anal. Appl. 318 (2006), 658–666.10.1016/j.jmaa.2005.05.085
  13. [13] DJOLOVIĆ, I.: On the space of bounded Euler difference sequences and some classes of compact operators, Appl. Math. Comput. 182 (2006), 1803–1811.
  14. [14] DJOLOVIĆ, I.—MALKOWSKY, E.: A note on compact operators on matrix domains, J. Math. Anal. Appl. 340 (2008), no. 1, 291–303.
  15. [15] DJOLOVIĆ, I.—MALKOWSKY, E.: Matrix transformations and compact operators on some new mth order difference sequence spaces, Appl. Math. Comput. 198 (2008), 700–714.
  16. [16] ET, M.—ÇOLAK, R.: On some generalized difference sequence spaces, Soochow J. Math. 21 (1995), 377–386
  17. [17] KARA, E. E.—BAS¸ARIR, M.: On some Euler B(m) difference sequence spaces and compact operators, J. Math. Anal. Appl. 379 (2011), 499–511.10.1016/j.jmaa.2011.01.028
  18. [18] KIZMAZ, H.: On certain sequence spaces, Canad. Math. Bull. 24 (1981), no. 2, 169–176.
  19. [19] KIRIS¸ÇI, M.—BAS¸AR, F.:, Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl. 60 (2010), 1299–1309.10.1016/j.camwa.2010.06.010
  20. [20] MADDOX, I. J.: Paranormed sequence spaces generated by infinite matrices,Proc. Camb. Phil. Soc. 64 (1968), 335–340.10.1017/S0305004100042894
  21. [21] MALKOWSKY, E.—PARASHAR, S. D.: Matrix transformations in scpace of bounded and convergent difference sequence of order m,Analysis 17 (1997), 87–97.10.1524/anly.1997.17.1.87
  22. [22] MALKOWSKY, E.—RAKOČEVIĆ, V.: An introduction into the theory of sequence spaces and measure of noncompactness, Zb. Rad, Belgrade 9 (2000), no. 17, 143–234.
  23. [23] MALKOWSKY, E.—RAKOČEVIĆ, V.: On matrix domains of triangles, Appl. Math. Comput. 189 (2007), no. 2, 1146–1163.
  24. [24] MALKOWSKY, E.—RAKOČEVIĆ, V.: The measure of noncompactness of linear operators between certain sequence spaces, Acta Sci. Math. (Szeged), 64 (1998), 151–171.
  25. [25] MALKOWSKY, E.—RAKOČEVIĆ, V.—ŽIVKOVIĆ, S.: Matrix transformations between the sequence spaces w0p(Λ), vp0(Λ), cp0(Λ)(1
  26. [26] MALKOWSKY, E.—SAVAS¸, E.: Matrix transformations between sequence spaces of generalized weighted mean, Appl. Math. Comput. 147 (2004), 333–345.
  27. [27] MURSALEEN, M.: Application of measure of noncompactness to infinite system of differential equations. Canadian Math. Bull. 2011, Paper: doi:10.4153/CMB-2011–170–7.10.4153/CMB-2011-170-7
  28. [28] MURSALEEN, M.—GANIE, A. H.—SHEIKH, N. A.: New type of difference sequence space and matrix transformation, Filomat 28 (2014), no. 7, 1381–1392.
  29. [29] MURSALEEN, M.—NOMAN, A. K.: Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means, Comput. Math. Appl. 60 (2010), no. 5, 245–1258.
  30. [30] MURSALEEN, M.—NOMAN, A. K.: Compactness by the Hausdorff measure of noncompactness, Nonlinear Anal. 73 (2010), no. 8, 2541–2557.
  31. [31] MURSALEEN, M.—NOMAN, A. K.: Compactness of matrix operators on some new difference sequence spaces, Linear Algebra Appl. Paper: doi: 10.1016/j.laa.2011.06.014.
  32. [32] MURSALEEN, M.—NOMAN, A. K.: On some new difference sequence spaces of non-absolute type, Math. Comput. Modelling 52 (2010), 603–617.10.1016/j.mcm.2010.04.006
  33. [33] OINAROV R.—TEMIRKHANOVA, A.: Boundedness and compactness of a class of matrix operators in weighted sequence spaces J. Math. Inequal. 2 (2008), no. 4, 555–570.
  34. [34] POLAT, H.—BAS¸AR, F.: Some Euler spaces of difference sequences of order m,Acta Math. Sci. 27 B (2007), no. 2, 254–266.
  35. [35] POLAT, H.—KARAKAYA, V.—S¸IMS¸EK, N.: Difference sequence spaces derived by generalized weighted mean, Appl. Math. Lett. 24 (2011), no. 5, 608–614.
  36. [36] RAKOČEVIĆ, V.: Measures of noncompactness and some applications, Filomat 12 (1998), 87–120.
  37. [37] STIEGLITZ, M.—TIETZ, H.: Matrix transformationen von folgenräumen eine ergebnisübersicht,Math. Z. 154 (1977), 1–16.10.1007/BF01215107
  38. [38]ŠALÁT, T.—TRIPATHY, B. C.—ZIMAN, M: On some properties of I-convergence, Tatra Mt. Math. Publ. 28 (2004), 279–286.
  39. [39] SHEIKH, N. A.—GANIE, A. H.: A new type of sequence space of non-absolute type and matrix transformation, WSEAS Transaction of Math. 8 (2013), no. 12, 852–859.
  40. [40] SHEIKH, N. A.—GANIE, A. H.: A new paranormed sequence space and some matrix transformation, Acta Math. Acad. Paedagogicae Nyiregyháziensis 28 (2012), 47–58.
  41. [41] SHEIKH, N. A.— JALAL, T.—GANIE, A. H.: New type of sequence spaces of non-absolute type and some matrix transformations, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 29 (2013), 51–66.
  42. [42] TRIPATHY, B. C.—ESI, A.—TRIPATHY, B. K.: On a new type of generalized difference Ce¸saro sequence spaces, Soochow J. Math. 31 (2005), no. 3, 333–340.
  43. [43] WILANSKY, A.: Summability Through Functional Analysis.In: North-Holland Math. Studies Vol. 85, Notas de Matemática [Mathematical Notes], Vol. 91. North-Holland Publishing Co., Amsterdam, 1984.
DOI: https://doi.org/10.2478/tmmp-2022-0013 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 165 - 182
Submitted on: Jul 10, 2022
Published on: Nov 29, 2022
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2022 Dowlath Fathima, Abdul Hamid Ganie, published by Slovak Academy of Sciences, Mathematical Institute
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