Journal of Mathematics and Applications
11/38, DOI: 10.7862/rf.2015.11
The random of lacunary statistical on χ2 over p-metric spaces defined by Musielak
N. Subramanian, R. Babu, P. Thirunavukkarasu
DOI: 10.7862/rf.2015.11
Abstract
Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. Recently Mohiuddine and Aiyup defined the notion of lacunary statistical convergence and lacunary statistical Cauchy in random 2-normed spaces. In this paper, we define and study the notion of lacunary statistical convergence and lacunary of statistical Cauchy sequences in random on χ2 over p− metric spaces defined by Musielak and prove some theorems which generalizes Mohiuddine and Aiyup results.
References
- M.Basarir and O.Solancan, On some double sequence spaces, J. Indian Acad. Math., 21(2) (1999), 193-200.
- T.J.I’A.Bromwich, An introduction to the theory of infinite series Macmillan and Co.Ltd., New York, (1965).
- G.H.Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917), 86-95.
- J.Lindenstrauss and L.Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390
- I.J.Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc, 100(1) (1986), 161-166.
- F.Moricz, Extentions of the spaces c and c0 from single to double sequences, Acta. Math. Hung., 57(1-2), (1991), 129-136.
- F.Moricz and B.E.Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc., 104, (1988), 283-294.
- B.C.Tripathy, On statistically convergent double sequences, Tamkang J. Math., 34(3), (2003), 231-237.
- A.Turkmenoglu, Matrix transformation between some classes of double sequences, J. Inst. Math. Comp. Sci. Math. Ser., 12(1), (1999), 23-31.
- P.K.Kamthan and M.Gupta, Sequence spaces and series, Lecture notes, Pure and Applied Mathematics, 65 Marcel Dekker, In c., New York , 1981.
- A.Gokhan and R.C¸olak, The double sequence spaces cP 2 (p) and cPB 2 (p), Appl. Math. Comput., 157(2), (2004), 491-501.
- A.Gokhan and R.C¸olak, Double sequence spaces ℓ∞ 2 , ibid., 160(1), (2005), 147153.
- M.Zeltser, Investigation of Double Sequence Spaces by Soft and Hard Analitical Methods, Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
- M.Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1), (2003), 223-231.
- B.Altay and F.BaS¸ar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1), (2005), 70-90.
- F.BaS¸ar and Y.Sever, The space Lp of double sequences, Math. J. Okayama Univ, 51, (2009), 149-157.
- N.Subramanian and U.K.Misra, The semi normed space defined by a double gai sequence of modulus function, Fasciculi Math., 46, (2010).
- J.Cannor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(2), (1989), 194-198.
- A.Pringsheim, Zurtheorie derzweifach unendlichen zahlenfolgen, Math. Ann., 53, (1900), 289-321.
- H.J.Hamilton, Transformations of multiple sequences, Duke Math. J., 2, (1936), 29-60.
- H.J.Hamilton, A Generalization of multiple sequences transformation, Duke Math. J., 4, (1938), 343-358.
-
H.J.Hamilton, Preservation of partial Limits in Multiple sequence transformations, Duke Math. J., 4, (1939), 293-297.
-
A.Wilansky, Summability through Functional Analysis, North-Holland Mathematical Studies, North-Holland Publishing, Amsterdam, Vol.85(1984).
About this Article
TITLE:
The random of lacunary statistical on χ2 over p-metric spaces defined by Musielak
AUTHORS:
N. Subramanian (1)
R. Babu (2)
P. Thirunavukkarasu (3)
AUTHORS AFFILIATIONS:
(1) Department of Mathematics, SASTRA University, Thanjavur-613 401, India
(2) Department of Mathematics, Shanmugha Polytechnic College, Thanjavur-613 401, India
(3) P.G. and Research Department of Mathematics, Periyar E.V.R. College (Autonomous) Tiruchirappalli–620 023, India
JOURNAL:
Journal of Mathematics and Applications
11/38
KEY WORDS AND PHRASES:
analytic sequence, double sequences, χ2 space, Musielak - modulus function, Random p− metric space, Lacunary sequence, Statistical convergence
FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/39
DOI:
10.7862/rf.2015.11
URL:
http://dx.doi.org/10.7862/rf.2015.11
RECEIVED:
2014-07-04
COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow