SavedAdd your journal

Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2017 / Volume: 35 Issue: 4

ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION

Vakeel A. Khan(Department of Mathematics, Aligarh Muslim University)0000-0002-4132-0954
Hira Fatıma(Department of Mathematics, Aligarh Muslim University)0000-0003-0407-6072
Sameera A. A. Abdullah(Department of Mathematics, Aligarh Muslim University)0000-0003-4094-2978
Kamal M. A. S. Alshlool(Department of Mathematics, Aligarh Muslim University)0000-0003-0029-2405
Pages
—
Publication Date
2017-12-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The sequence space BV_(σ )was introduced and studied by Mursaleen [Houston J.
📊
Key Findings & Data:Math. 9, 505-509 (1983; Zbl 0542.40003)].
💡
Conclusion & Impact:Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bounded variation · invariant mean · σ-Bounded variation

Abstract

The sequence space BV_(σ )was introduced and studied by Mursaleen [Houston J. Math. 9, 505-509 (1983; Zbl 0542.40003)]. The main aim of this paper is to study some new double sequence spaces of invariant means defined by ideal and modulus function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.

🔖

Cite This Article

Khan, V. A., Fatıma, H., Abdullah, S. A. A., Alshlool, K. M. A. S. (2017). ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. Sigma Mühendislik ve Fen Bilimleri Dergisi, Volume: 35 Issue: 4. https://ajindex.com/articles/1345137

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (37)

  1. Ahmad,Z.U., and Mursaleen,M.(1988), “An application of Banach limits,” Proc.Amer. Math. soc 103(1), 244-246. Banach,S.(1986), “Theorie des operations lineaires,” Warszawa, (1932)103, 244-246.
  2. Fast,H.(1951), “Sur la convergence statistique,” Colloq. Math. 2, 241-244.
  3. Fridy,J.A.(1985), “On statistical convergence,” Analysis. 5, 301-313.
  4. Gramsch,B.(1967), “Die Klasse metrisher linearer Raume L(Á),” Math. Ann. 171, 61-78.
  5. Habil, E.D., 2006, “Double sequences and double series,” The Islamic University Journal,Series of Natural Studies and Engineering, vol. 14, pp, 1-33.
  6. Hazarika, B., Karan, T. and Singh,B.K. (2014), “Zweier Ideal convergent sequence space defined by Orlicz function,” Journal of mathematics and com- puter science 8, 307-318
  7. Khan,V.A.(2008), “On a new sequence space defined by Orlicz function,” Communications de la Faculté des Sciences de l'Université d'Ankara SériesA1.57, 25-33.
  8. Khan, V. A. and Ebadullah, K. (2013), “On some new convergent sequence space,” Mathematics, Aeterna 3(2)151-159.
  9. Khan, V. A. and Ebadullah, K. (2012), “On a new I-convergent sequence space,” Analysis 32, 199-208.
  10. Khan, V.A., Fatima, H., Abdullaha, S.A.A., Khan, M.D. (2016), “On a New BVσ-I-Convergent Double Sequence Spaces,” Theory and Application of mathematics and computer science 6 (2), 187-197.
  11. Khan,V.A., Ebadullah,K.(2012), “I-convergent sequences spaces defined by sequence of moduli,” Journal of Mathematical and Computational Science 2 (2), 265-273.
  12. Khan, V.A, Esi, A. and Shafiq, M.(2014), “On some BV_σ I-convergent sequence spaces Defined by modulus function,” Global Journal of Mathematical Analysis, 2(2) 17-27.
  13. King, J.P.(1966), “Almost summable Sequences,” Proc.Amer. Math. soc.17, 1219-1225.
  14. Kayaduman, K., and Sengönül, M. (2014), “Some New Type Sigma Convergent Sequence Spaces and Some New Inequalities,” Scientific world journal 589765.
  15. Kostyrko,P.,Ŝalát, T. and Wilczyński,W.(2000), “I convergence,” Real Analysis Exchange. 26(2), 669-686.
  16. Kostyrko,P.,Mańaj, M. and Salát,T., “Statistical convergence and I-convergence,” Real Analysis Exchange.
  17. KÄothe, G. (1970), “Topological Vector spaces.1.” Springer, Berlin.
  18. Lorentz, G.G. (1948), “A contribution to the theory of divergent series,” Acta Math, 80, 167-190.
  19. Mursaleen, M.(1983), “On some new invariant matrix methods of summability,” The Quart. J. Math., 34(133), 77-86.
  20. Mursaleen, M.(1983), “Matrix transformation between some new sequence spaces,” Houston J. Math.9, 505-509.
  21. Maddox, I.J.(1970), “Elements of Functional Analysis,” Cambridge University Press.
  22. Maddox, I.J.(1968), “Paranormed sequence spaces generated by infinite matrices,” Math. Proc. Cambridge Philos. Soc. 64,335340.
  23. Maddox, I.J.(1986), “Sequence spaces defined by a modulus,” Math. Camb. Phil. Soc.100, 161-166.
  24. Nakano, H.(1951), “Modular sequence spaces.” Proc. Jpn. Acad. Ser. A Math. Sci. 27, 508512.
  25. Raimi, R.A.(1963), “Invariant means and invariant matrix methods of summability,” Duke J. Math.30, 81-94.
  26. Ruckle, W.H.(1968), “On perfect Symmetric BK-spaces”, Math.Ann. 175, 121-126.
  27. Ruckle, W.H.(1967), “Symmetric coordinate spaces and symmetric bases”, Canad.J.Math. 19, 828-838.
  28. Ruckle, W.H.(1973), “FK-spaces in which the sequence of coordinate vectors is bounded,” Canad.J. Math.25 (5) 973-975.
  29. Saláat, T., Tripathy, B.C. and Ziman, M. (2004), “On some properties of I-convergence,” Tatra Mt. Math. Publ. 28, 279-286.
  30. Salát, T., Tripathy, B.C and Ziman, M.(2005), “On I-convergence field,” Ital. J. Pure Appl. Math. 17, 45-54.
  31. Tripathy, B.C and Hazarika, B.(2009), “Paranorm I-convergent sequence spaces,” Math. Slovaca. 59(4), 485-494.
  32. Tripathy, B.C., Hazarika, B.(2008), “I-convergent sequence spaces associated with multiplier sequences,” Math. Ineq. Appl. 11(3), 543548.
  33. Tripathy,B.C and Hazarika,B.(2011), “Some I-Convergent sequence spaces defined by Orlicz function,” Acta Mathematicae Applicatae Sinica.27(1),149-154.
  34. Khan, V.A, Esi, A. and Shafiq, M.(2014), “On some BV_σ I-convergent sequence spaces Defined by modulus function,” Global Journal of Mathematical Analysis, 2(2) 17-27.
  35. Kostyrko,P.,Ŝalát, T. and Wilczyński,W.(2000), “I convergence,” Real Analysis Exchange. 26(2), 669-686.
  36. KÄothe, G. (1970), “Topological Vector spaces.1.” Springer, Berlin.
  37. Salát, T., Tripathy, B.C and Ziman, M.(2005), “On I-convergence field,” Ital. J. Pure Appl. Math. 17, 45-54.