# A CONNECTION BETWEEN INFINITE MATRIX AND SEMINORM TO ORIGINATE ORLICZ VECTOR VALUED SEQUENCE SPACES AND THEIR STATISTICAL CONVERGENCE

 Title A CONNECTION BETWEEN INFINITE MATRIX AND SEMINORM TO ORIGINATE ORLICZ VECTOR VALUED SEQUENCE SPACES AND THEIR STATISTICAL CONVERGENCE Publication Type Journal Article Year of Publication 2018 Authors RAJ, KULDIP, SHARMA, CHARU Volume 22 Issue 2 Start Page 163 Pagination 24 Date Published 2018 ISSN 1083-2564 AMS 40A05, 40A35, 46C45 Abstract In the present paper we introduce and study some vector valued sequence spaces by using infinite matrix, seminorm and a sequence of Orlicz functions with real n-normed space as base space. We make an effort to study some topological and algebraic properties of these spaces. We also show that these spaces are complete paranormed spaces when the base space is n-Banach space and investigate some inclusion relations between the spaces. Finally, we study statistical convergence of these spaces. URL https://acadsol.eu/en/articles/22/2/3.pdf DOI 10.12732/caa.v22i2.3 Refereed Designation Refereed Full Text REFERENCES [1] R. C¸ olak, On some generalized sequence spaces, Comm. Fasc. Sci. Univ. Ankara Ser. A1 Math. Statist., 38 (1989), 35-46. INFINITE MATRIX AND SEMINORM [2] J.S. Connor, The statistical and strong p-Cesaro convergence of sequeces, Analysis, 8 (1988), 47-63. [3] N. R. Das and A. Choudhary, Matrix transformation of vector valued sequence spaces, Bull. Calcutta Math. Soc., 84 (1992), 47-54. [4] H. Dutta, Characterization of certain matrix classes involving generalized difference summability spaces, Appl. Sci., 11 (2009), 60-67. [5] M. Et, Y. Altin, B. Choudhary and B.C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Inequal. Appl., 9 (2006), 335-342. [6] M. Et and R. C¸ olak, On some generalized difference sequence spaces, Soochow. J. Math., 21 (1995), 377-386. [7] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. [8] J. A. Fridy, On the statistical convergence, Analysis, 5 (1985), 301-303. [9] S. G¨ahler, Linear 2-normietre Rume, Math. Nachr., 28 (1965), 1-43. [10] G. Goes and S. Goes, Sequence of bounded variation and sequences of Fourier coeffficients, Math. Zeit, 118 (1970), 93-102. [11] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639. [12] P. K. Kamthan and M. Gupta, Sequence Spaces and Series, M. Dekker, New York, 1981. [13] H. Kızmaz, On certain sequence spaces, Canad. Math-Bull., 24 (1981), 169-176. [14] P. K´orus, On Λ2 -strong convergence of numerical sequences revisited, Acta Math. Hungar., 148 (2016), 222-227. [15] P. K´orus, On the uniform convergence of double sine series with generalized monotone coefficients, Period. Math. Hungar., 63 (2011), 205-2014. [16] P. K´orus, On the uniform convergence of special sine integrals, Acta Math. Hungar., 133 (2011), 82-91. K. RAJ AND C. SHARMA [17] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390. [18] A. Misiak, n-Inner product spaces, Math. Nachr., 140 (1989), 299-319. [19] F. M´oricz, On the uniform convergence of sine integrals, J. Math. Anal. Appl., 354 (2009), 213-219. [20] M. Mursaleen, λ−statistical convergence, Math. Slovaca, 50 (2000), 111- 115. [21] M. Mursaleen and O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223-231. [22] K. Raj and C. Sharma, Applications of strongly convergent sequences to Fourier series by means of modulus functions, Acta Math. Hungar., 150 (2016), 396-411. [23] K. Raj and S. Jamwal, On some generalized statistical convergent sequence spaces, Kuwait J. Sci., 42 (2015), 86-104. [24] K. Raj, S. Jamwal and S. K. Sharma, New classes of generalized sequence spaces defined by an Orlicz function, J. Comput. Anal. Appl., 15 (2013), 730-737. [25] A. Ratha and P. D. Srivastava, On some vector valued sequence spaces L (p) ∞ (Ek,Λ), Ganita, 47 (1996), 1-12. [26] E. Sava¸s and M. Mursaleen, Matrix transformations in some sequence spaces, Istanb. Univ. Fen Fak. Mat. Derg., 52 (1993), 1-5. [27] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375. [28] B. C. Tripathy and M. Sen, Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences, Soochow J. Math., 29 (2003), 379-391. [29] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematics Studies, 85, Amsterdam-New York-Oxford, 1984.