New spaces over modulus function
DOI:
https://doi.org/10.5269/bspm.53027Abstract
Our main aim of this paper is to introduce some new techniques of spaces using modulus function. Some of basic inclusion properties will be taken care of.
References
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8. A. H. Ganie and A. Antesar, Certain spaces using â–³- operator, Adv. Stud. Contemp. Math. (Kyungshang), 30(1)(2020), 17-27.
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14. K. G. Gross Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223- 238. https://doi.org/10.1006/jmaa.1993.1398
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25. W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canand. J. Math., 25, 973-978, (1973). https://doi.org/10.4153/CJM-1973-102-9
26. M. Sengonul and F. Basar, Some new Cesaro sequences spaces of non-absolute type, which include the spaces co and c, Soochow J. Math., 1, 107-119, (2005).
27. N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 28, 47-58, (2012).
28. N. A. Sheikh and A. H. Ganie, New paranormed sequence space and some matrix transformations, WSEAS Transaction of Math., 8(12), 852-859, (2013).
29. N. A. Sheikh, T. Jalal and A. H. Ganie, New type of sequence spaces of non-absolute type and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 29, 51-66, (2013).
30. O. Toeplitz, Uber allegemeine Lineare mittelbildungen , Prace Math. Fiz., 22, 113-119, (1991).
31. C. S. Wang, On Norlund sequence spaces, Tamkang J. Math., 9, 269-274, (1978).
32. A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, Amsterdam - New York - Oxford, (1984).
2. B. Altay and F. Ba¸sar, On the paranormed Riesz sequence space of nonabsolute type, Southeast Asian Bull. Math., 26, 701-715, (2002).
3. C. Aydin and F. Ba¸sar, Some new paranormed sequence spaces, Inf. Sci., 160, 27-40, (2004). https://doi.org/10.1016/j.ins.2003.07.009
4. M. Basarir and M. Ozturk, On the Riesz difference sequence space, Rendiconti del Cirocolo di Palermo, 57, 377-389, (2008). https://doi.org/10.1007/s12215-008-0027-2
5. B. Choudhary and S. K. Mishra, On K¨othe Toeplitz Duals of certain sequence spaces and matrix Transformations, Indian, J. Pure Appl. Math., 24(4), 291-301, (1993).
6. A. H. Ganie, Some new approach of spaces of non-integral order, J. Nonlinear Sci, Appl., 14(2), 89-96, (2021). https://doi.org/10.22436/jnsa.014.02.04
7. A. H. Ganie, Riesz spaces using modulus function, Int. jour. Math. Mod. Meth. Appl. Sci., 14, 20-23, (2020).
8. A. H. Ganie and A. Antesar, Certain spaces using â–³- operator, Adv. Stud. Contemp. Math. (Kyungshang), 30(1)(2020), 17-27.
9. A. H. Ganie and S. A. Lone, Some sequence spaces of sigma means defined by Orlicz function, Appl. Math. Inf. Sci., (accepted 2020).
10. A. H. Ganie and N. A. Sheikh, On some new sequence space of non-absolute type and matrix transformations, J. Egyptain Math. Soc., 21, 34-40, (2013). https://doi.org/10.1016/j.joems.2013.01.006
11. A. H. Ganie, N. A. Sheikh and T. Jalal, On some new spaces of invariant means with respect to modulus function, The inter. Jou. Modern Math. Sciences, USA, 13(3), 210-216, (2015).
12. A. H. Ganie, A. Mobin N. A. Sheikh and T. Jalal, New type of Riesz sequence space of non-absolute type, J. Appl. Comput. Math., 5(1), 1-4, (2016).
13. A. H. Ganie, Mobin Ahmad, N. A. Sheikh, T.Jalal and S. A. Gupkari, Some new type of difference sequence space of non-absolute type, Int. J. Modern Math.Sci., 14(1), 116-122, (2016).
14. K. G. Gross Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223- 238. https://doi.org/10.1006/jmaa.1993.1398
15. T. Jalal, S. A. Gupkari and A. H. Ganie, Infinite matrices and sigma convergent sequences, Southeast Asian Bull. Math., 36, 825-830, (2012).
16. C. G. Lascarides and I. J. Maddox, Matrix transformations between some classes of sequences, Proc. Camb. Phil. Soc., 68, 99-104, (1970). https://doi.org/10.1017/S0305004100001109
17. I. J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc., 64, 335-340, (1968). https://doi.org/10.1017/S0305004100042894
18. I. J. Maddox, Elements of Functional Analysis, 2nded., The University Press, Cambridge, (1988).
19. E. Malkowsky, Matrix transformations between spaces of absolutely and strongly summable sequences, Habilitationsschrift, Giessen (1988). https://doi.org/10.1524/anly.1988.8.34.325
20. M. Mursaleen, F. Ba¸sar and B. Altay, On the Euler sequence spaces which include the spaces lp and l∞-II, Nonlinear Anal., 65, 707-717, (2006). https://doi.org/10.1016/j.na.2005.09.038
21. M. Mursaleen, A. H. Ganie and N. A. Sheikh, New type of difference sequence space and matrix transformation, FILOMAT, 28(7), 1381-1392, (2014). https://doi.org/10.2298/FIL1407381M
22. N. Nakano, Cancave modulars, J. Math. Soc. Japan, 5, 29-49, (1953). https://doi.org/10.2969/jmsj/00510029
23. P.-N. Ng and P.-Y. Lee, Cesaro sequences spaces of non-absolute type, Comment. Math. Prace Mat. 20(2), 429-433, (1978).
24. G. M. Petersen, Regular matrix transformations, Mc Graw-Hill, London, (1966).
25. W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canand. J. Math., 25, 973-978, (1973). https://doi.org/10.4153/CJM-1973-102-9
26. M. Sengonul and F. Basar, Some new Cesaro sequences spaces of non-absolute type, which include the spaces co and c, Soochow J. Math., 1, 107-119, (2005).
27. N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 28, 47-58, (2012).
28. N. A. Sheikh and A. H. Ganie, New paranormed sequence space and some matrix transformations, WSEAS Transaction of Math., 8(12), 852-859, (2013).
29. N. A. Sheikh, T. Jalal and A. H. Ganie, New type of sequence spaces of non-absolute type and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 29, 51-66, (2013).
30. O. Toeplitz, Uber allegemeine Lineare mittelbildungen , Prace Math. Fiz., 22, 113-119, (1991).
31. C. S. Wang, On Norlund sequence spaces, Tamkang J. Math., 9, 269-274, (1978).
32. A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, Amsterdam - New York - Oxford, (1984).
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2022-12-21
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