On Zweier generalized difference ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function
DOI:
https://doi.org/10.5269/bspm.v35i2.29077Abstract
Let $\mathbf{M}=(M_k)$ be a Musielak-Orlicz function. In this article, we introduce a new class of ideal convergent sequence spaces defined by Musielak-Orlicz function, using an infinite matrix, and a generalized difference matrix operator $B_{(i)}^{p}$ in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We obtain some relations related to these sequence spaces.
References
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35. B.C. Tripathy, A. Esi, B. K. Tripathy, On a new type of generalized difference Cesà ro sequence spaces, Soochow J. Math; 31(2005),333-340.
36. B. C. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009) 485-494.
37. B. C. Tripathy, B. Hazarika, Some I-convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sinica, 27(1) (2011) 149-154.
38. B.C. Tripathy, M. Et, Y. Altin, Generalized difference sequence spaces defined by Orlicz function in a locally convex space, J. Anal. Appl., 3(1)(2003) 175-192.
2. M. Basarir, M. Kayikçi, On the generalized Bm-Riesz difference sequence spaces and - property, J. Inequa. Appl., Vol 2009(2009), Artcle ID 385029, 18 pages.
3. M. Basarir, S. Konca, E. E. Kara, Some generalized difference statistically convergent sequence spaces in 2-normed space, J. Inequa. Appl., 2013, 2013:177.
4. H. Cartan, Filters et ultrafilters, C. R. Acad. Sci. Paris 205 (1937), 777-779.
5. H. Dutta, Some statistically convergent difference sequence spaces defined over real 2-normed linear space, Appl. Sci., 12(2010), 37-47.
6. A. Esi, Strongly almost summable sequence spaces in 2-normed spaces defined by ideal convergence and an Orlicz function, Stud. Univ. Babes-Bolyai Math. 57(1)(2012), 75-82
7. A. Esi and A. SapsÄszoglu, On some lacunary -strong Zweier convergent sequence spaces, Romai J., 8(2)(2012), 61-70.
8. M. Et, R. Çolak, On generalized difference sequence spaces, Soochow J. Math., 21(4)(1995) 377-386.
9. M. Et, Y. Altin, B. Choudhary, B. C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Inequa. Appl., 9(2)(2006) 335-342.
10. B. Hazarika, Some lacunary difference sequence spaces defined by Musielak-Orlicz functions, Asia-European J. Math., 4(4)(2011), 613-626.
11. B. Hazarika, E. Savas, Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by sequence of Orlicz functions, Math. Comput. Modelling, 54(11-12)(2011), 2986-2998.
12. B. Hazarika, On generalized difference ideal convergence in random 2-normed spaces, Filomat, 26(6) (2012), 1265-1274.
13. B. Hazarika, On fuzzy real valued generalized difference I-convergent sequence spaces defined by Musielak-Orlicz function, J.. Intell. Fuzzy Systems, 25(1)(2013), 9-15.
14. B. Hazarika, Classes of generalized difference ideal convergent sequences of fuzzy numbers, Ann. Fuzzy Math. Inform., 7(1)(2014), 155-172.
15. B. Hazarika, K. Tamang and B. K. Singh, Zweier Ideal Convergent Sequence Spaces Defined by Orlicz Function, The J. Math. Comput. Sci., 8(3)(2014), 307-318.
16. B. Hazarika, Karan Tamang and B. K. Singh, On Paranormed Zweier Ideal Convergent Sequence Spaces Defined By Orlicz Function, J. Egyptian Math. Soc., 22(3)(2014), 413-419.
17. B. Hazarika, Strongly almost ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function, Iranian J. Math. Sci. Inform., 9(2)(2014), 15-35.
18. B. Hazarika and Karan Tamang, On Zweier Sequence Spaces and de la Vallée-Poussin mean of order and some geometric properties, Bol. Soc. Port. Mat., 34(2)(2016), 189-195 (in press).
19. Y. Fadile Karababa and A. Esi, On some strong Zweier convergent sequence spaces, Acta Universitatis Apulensis,29(2012), 9-15.
20. V. A. Khan and Q. M. D. Lohani, Some new difference sequence spaces defined by Musielak-Orlocz function, Thai J. Math., 6(1) (2008) 215-223.
21. V. A. Khan, K. Ebadullah, A. Esi, N. Khan, M. Shafiq, On Paranorm Zweier I-convergent sequences spaces, Inter. J. Analysis, Vol. 2013 (2013), Article ID 613501, 6 pages.
22. V.A.Khan, K. Ebadullah, A. Esi and M. Shafiq, On some Zweier I-convergent sequence spaces defined by a modulus function, Afrika. Mat. DOI 10.1007/s13370-013-0186-y (2013).
23. H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(2)(1981)169-176.
24. P. Kostyrko, T. Salát, and W. Wilczynski, I-convergence, Real Analysis Exchange, 26(2)(2000-2001),669-686.
25. M.A. Krasnoselski, Y.B. Rutitsky, Convex Functions and Orlicz Functions, P. Noordhoff, Groningen, Netherlands, 1961.
26. K Lindberg, On subspaces of Orlicz sequence spaces, Studia Math., 45(1973) 119-146.
27. J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10(1971) 379-390.
28. M. Mursaleen, M. A. Khan, Qamaruddin, Difference sequence spaces defined by Orlicz functions, Demonstratio. Math., 32 (1999) 145-150.
29. H. Nakano, Modular sequence spaces, Proc. Japan Acad., 27(1951), 508-512.
30. F. Nuray and William H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl., 245(2000), 513-527.
31. S. D. Parashar, B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25(4)(1994) 419-428.
32. W. H. Ruckle, FK-spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25 (1973) 973-978.
33. M. Sengönül, On The Zweier Sequence Space. Demonstratio Math. Vol.XL No. (1)(2007), 181-196.
34. B. C. Tripathy, A. Esi, A new type of difference sequence spaces, Inter. J. Sci. Tech., 1(1)(2006), 11-14.
35. B.C. Tripathy, A. Esi, B. K. Tripathy, On a new type of generalized difference Cesà ro sequence spaces, Soochow J. Math; 31(2005),333-340.
36. B. C. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009) 485-494.
37. B. C. Tripathy, B. Hazarika, Some I-convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sinica, 27(1) (2011) 149-154.
38. B.C. Tripathy, M. Et, Y. Altin, Generalized difference sequence spaces defined by Orlicz function in a locally convex space, J. Anal. Appl., 3(1)(2003) 175-192.
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