Ideal Convergent Sequence Spaces with Respect to Invariant Mean and a Musielak-Orlicz Function Over n-Normed Spaces
Main Article Content
Abstract
In the present paper we defined I-convergent sequence spaces with respect to invariant mean and a Musielak-Orlicz function M = (M_k) over n-normed spaces. We also make an effort to study some topological properties and prove some inclusion relation between these spaces.
Article Details
References
- P. Das, P. Kostyrko, W. Wilczynski and P. Malik, I and I* convergence of double sequences, Math. Slovaca, 58 (2008), 605-620.
- P. Das and P.Malik, On the statistical and I- variation of double sequences, Real Anal. Exch. 33 (2)(2007-2008), 351-364.
- S. G ¨ahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1-43.
- H. Gunawan, On n-Inner Product, n-Norms, and the Cauchy-Schwartz Inequality, Sci. Math. Jap., 5 (2001), 47-54.
- H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc., 64 (2001), 137-147.
- H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639.
- E. E. Kara, M. Da ¸stan and M. ¨Ilkhan, On almost ideal convergence with respect to an Orlicz function, Konuralp J. Math. 4 (2016), 87-94.
- P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exch. 26 (2) (2000), 669-686.
- V. Kumar, On I and I* convergence of double sequences, Math. Commun., 12 (2007), 171-181.
- J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10(1971), 345-355.
- G. G. Lorentz, A contribution to the theory of divergent series, Acta Math. 80(1948), 167-190.
- I. J. Maddox, Spaces of strongly summable sequence, Q. J. Math; 18(1967), 345-355.
- L. Maligranda,Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989.
- A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319.
- M. Mursaleen and A. Alotaibi, On I-convergence in radom 2-normed spaces, Math. Slovaca, 61(6)(2011), 933-940.
- M. Mursaleen, S. A. Mohiuddine and O. H. H. Edely, On ideal convergence of double sequences in intuitioistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010), 603-611.
- M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(64)(4) (2010), 359-371.
- M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62(2012), 49-62.
- M. Mursaleen and S. K. Sharma, Spaces of ideal convergent sequences, World Sci. J. 2014(2014), Art. ID 134534.
- J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Springer-Verlag Berlin Heidelberg, (1983).
- K. Raj and S. K. Sharma, Ideal convergent sequence spaces defined by a Musielak-Orlicz function, Thai. J. Math., 11 (2013), 577-587.
- K. Raj and S. K. Sharma, Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz functions, Acta Univ. Sapientiae Math., 3 (2011), 97-109.
- K. Raj and S. K. Sharma, Some generalized difference double sequence spaces defined by a sequence of Orlicz-function, Cubo, 14 (2012), 167-189.
- K. Raj and S. K. Sharma, Some multiplier sequence spaces defined by a Musielak-Orlicz function in n-normed spaces, N. Z. J. Math. 42 (2012), 45-56.
- A. S ¸ahiner, M. G ¨urdal, S. Saltan and H. Gunawan, On ideal convergence in 2-normed spaces, Taiwanese J. Math., 11 (2007), 1477-1484.
- P. Schaefer, Invariant matrices and invariant means, Proc. Amer. Math. Soc.; 36(1972), 104-110.
- B. C. Tripathy and B. Hazarika, Some I-convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sin. Engl. Ser. 27 (2011), 149-154.