# Some sequence spaces over $n$-normed spaces defined by fractional difference operator and Musielak-Orlicz function

## Main Article Content

## Abstract

In the present paper we introduce some sequence spaces over $n$-normed spaces defined by fractional difference operator and Musielak-Orlicz function $\mathcal{M} = (\mathfrak{F}_i)$. We also study some topological properties and prove some inclusion relations between these spaces.

## Article Details

## References

[1] A.H.A. Bataineh, On some difference sequences defined by a sequence of Orlicz functions, Soo- chow J. Math., 33 (2007), 761–769. Google Scholar

[2] P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219 (2013), 9737–9742. Google Scholar

[3] T. Bilgin, Some new difference sequences spaces defined by an Orlicz function, Filomat, 17 (2003), 1–8. Google Scholar

[4] M. Et and R. C ̧olak, On some generalized difference sequence spaces, Soochow. J. Math., 21 (1995),377–386. Google Scholar

[5] A. R. Freedman, J. J. Sember and M. Raphael, Some Ces`aro-type summability spaces, Proc. London Math. Soc., 37 (1978), 508–520. Google Scholar

[6] S. G ̈ahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1–43. Google Scholar

[7] H. Gunawan, On n-inner product, n-norms, and the Cauchy-Schwartz inequality, Scientiae Math. Jpn, 5 (2001), 47–54. Google Scholar

[8] H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc., 64 (2001), 137–147. Google Scholar

[9] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631–639. Google Scholar

[10] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169–176. Google Scholar

[11] K. Raj, S.A. Mohiuddine and M. Ayman Mursaleen, Some generalized sequence spaces of Invariant means defined by ideal and modulus functions in n-normed space, Italian Jour. Pure Appl. Math., 39 (2018). Google Scholar

[12] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379–390. Google Scholar

[13] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345–355. Google Scholar

[14] I. J. Maddox, On strong almost convergence, Math. Proc. Camb. Phil. Soc., 85 (1979), 345–350. Google Scholar

[15] L. Maligranda, Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989. Google Scholar

[16] E. Malkowsky and V. Veliˇckovic ̇, Topologies of some new sequence spaces, their duals, and the graphical representations of neighbourhoods, Topology Appl., 158 (2011), 1369–1380. Google Scholar

[17] E. Malkowsky and V. Veliˇckovic ̇, Some new sequence spaces, their duals and a connection with Wulff’s crystal, Match Commun. Math. Comput. Chem., 67 (2012), 589–607. Google Scholar

[18] E. Malkowsky, M. Mursaleen and S. Suantai, The dual spaces of sets of difference sequences of order m and matrix transformations, Acta Math. Sin. (Engl. Ser.) 23 (2007), 521–532. Google Scholar

[19] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299–319. Google Scholar

[20] M. Ayman Mursaleen, On s-convergence by de la Vall ee Poussin mean and matrix transforma- tions, Jour. Inequ. Special Functions, 8(3) (2017) 119-124. Google Scholar

[21] M. Mursaleen, Generalized spaces of difference sequences, J. Math. Anal. Appl.,203 (1996), 738–745. Google Scholar

[22] M. Mursaleen and S. K. Sharma, Entire sequence spaces defined on locally convex Hausdorff topological space, Iranian Journal of Science and Technology, 38 (2014), 105–109. Google Scholar

[23] M. Mursaleen, A. Alotaibi and S. K. Sharma, New classes of generalized seminormed difference sequence spaces, Abstract and Applied Analysis, 2014, 11 pages. Google Scholar

[24] M. Mursaleen, A. Alotaibi and S. K. Sharma, Some new lacunary strong convergent vector-valued sequence spaces, Abstract and Applied Analysis, 2014, 9 pages. Google Scholar

[25] J. Musielak,Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034 (1983). Google Scholar

[26] S. D. Parashar and B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25 (1994), 419–428. Google Scholar

[27] K. Raj and S. K. Sharma, A new sequence space defined by a sequence of Orlicz functions over n−normed spaces, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 51 (2012), 89–100. Google Scholar

[28] K. Raj and S. K. Sharma, So me multiplier generalized difference sequence spaces over n-normed spaces defined by a Musielak-Orlicz function, Siberian Advances in Mathematics, 24 (2014), 193–203. Google Scholar

[29] A. Wilansky, Summability through functional analysis, North-Holland Math. Stud. 85 (1984). Google Scholar