zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some spaces of double sequences obtained through invariant mean and related concepts. (English) Zbl 1277.46003
Summary: We introduce some double sequence spaces involving the notions of invariant mean (or $\sigma$-mean) and $\sigma$-convergence for double sequences, while the idea of $\sigma$-convergence for double sequences was introduced by {\it C. Çakan} et al. [Appl. Math. Lett. 19, No. 10, 1122--1128 (2006; Zbl 1122.40004)] by using the notion of invariant mean. We determine here some inclusion relations and topological results for these new double sequence spaces.
MSC:
46A45Sequence spaces
40A05Convergence and divergence of series and sequences
40B05Multiple sequences and series
WorldCat.org
Full Text: DOI
References:
[1] A. Pringsheim, “Zur Theorie der zweifach unendlichen Zahlenfolgen,” Mathematische Annalen, vol. 53, no. 3, pp. 289-321, 1900. · Zbl 31.0249.01 · doi:10.1007/BF01448977
[2] M. Mursaleen, “On some new invariant matrix methods of summability,” The Quarterly Journal of Mathematics, vol. 34, no. 133, pp. 77-86, 1983. · Zbl 0539.40006 · doi:10.1093/qmath/34.1.77
[3] P. Schaefer, “Infinite matrices and invariant means,” Proceedings of the American Mathematical Society, vol. 36, pp. 104-110, 1972. · Zbl 0255.40003 · doi:10.2307/2039044
[4] G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167-190, 1948. · Zbl 0031.29501 · doi:10.1007/BF02393648
[5] S. A. Mohiuddine, “An application of almost convergence in approximation theorems,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1856-1860, 2011. · Zbl 1252.41022 · doi:10.1016/j.aml.2011.05.006
[6] C. \cCakan, B. Altay, and M. Mursaleen, “The \sigma -convergence and \sigma -core of double sequences,” Applied Mathematics Letters, vol. 19, no. 10, pp. 1122-1128, 2006. · Zbl 1122.40004 · doi:10.1016/j.aml.2005.12.003
[7] M. Mursaleen and S. A. Mohiuddine, “Double \sigma -multiplicative matrices,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 991-996, 2007. · Zbl 1107.40004 · doi:10.1016/j.jmaa.2006.04.081
[8] M. Mursaleen and S. A. Mohiuddine, “Regularly \sigma -conservative and \sigma -coercive four dimensional matrices,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1580-1586, 2008. · Zbl 1155.40303 · doi:10.1016/j.camwa.2008.03.007
[9] M. Mursaleen and S. A. Mohiuddine, “On \sigma -conservative and boundedly \sigma -conservative four-dimensional matrices,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 880-885, 2010. · Zbl 1189.40005 · doi:10.1016/j.camwa.2009.10.006
[10] F. Móricz and B. E. Rhoades, “Almost convergence of double sequences and strong regularity of summability matrices,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 2, pp. 283-294, 1988. · Zbl 0675.40004 · doi:10.1017/S0305004100065464
[11] I. J. Maddox, “A new type of convergence,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 83, no. 1, pp. 61-64, 1978. · Zbl 0392.40001 · doi:10.1017/S0305004100054281
[12] M. Ba\csarir, “On the strong almost convergence of double sequences,” Periodica Mathematica Hungarica, vol. 30, no. 3, pp. 177-181, 1995. · doi:10.1007/BF01876616
[13] M. Mursaleen and S. A. Mohiuddine, “Some new double sequence spaces of invariant means,” Glasnik Matemati\vcki, vol. 45, no. 65, pp. 139-153, 2010. · Zbl 1195.46005 · doi:10.3336/gm.45.1.11
[14] A. Alotaibi, M. Mursaleen, and M. A. Alghamdi, “Invariant and absolute invariant means of double sequences,” Journal of Function Spaces and Applications, vol. 2012, Article ID 465364, 9 pages, 2012. · Zbl 1260.40005 · doi:10.1155/2012/465364
[15] C. Aydin and F. Ba\csar, “Some new paranormed sequence spaces,” Information Sciences, vol. 160, no. 1-4, pp. 27-40, 2004. · Zbl 1049.46002 · doi:10.1016/j.ins.2003.07.009
[16] C. Aydın and F. Ba\csar, “Some new difference sequence spaces,” Applied Mathematics and Computation, vol. 157, no. 3, pp. 677-693, 2004. · Zbl 1072.46007 · doi:10.1016/j.amc.2003.08.055
[17] F. Ba\csar and M. Kiri\cs\cci, “Almost convergence and generalized difference matrix,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 602-611, 2011. · Zbl 1217.40001 · doi:10.1016/j.camwa.2010.12.006
[18] C. \cCakan, B. Altay, and H. Co\cskun, “\sigma -regular matrices and a \sigma -core theorem for double sequences,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 1, pp. 51-58, 2009. · Zbl 1182.40003
[19] G. Das and S. K. Sahoo, “On some sequence spaces,” Journal of Mathematical Analysis and Applications, vol. 164, no. 2, pp. 381-398, 1992. · Zbl 0778.46011 · doi:10.1016/0022-247X(92)90122-T
[20] K. Kayaduman and C. \cCakan, “The cesáro core of double sequences,” Abstract and Applied Analysis, vol. 2011, Article ID 950364, 9 pages, 2011. · doi:10.1155/2011/950364
[21] M. Mursaleen, “Almost strongly regular matrices and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 523-531, 2004. · Zbl 1043.40002 · doi:10.1016/j.jmaa.2004.01.014
[22] M. Mursaleen, “Some matrix transformations on sequence spaces of invariant means,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 259-264, 2009. · Zbl 1196.40005
[23] M. Mursaleen and O. H. H. Edely, “Almost convergence and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 532-540, 2004. · Zbl 1043.40003 · doi:10.1016/j.jmaa.2004.01.015
[24] M. Mursaleen, A. M. Jarrah, and S. A. Mohiuddine, “Almost convergence through the generalized de la Vallée-Poussin mean,” Iranian Journal of Science and Technology. Transaction A, vol. 33, no. 2, pp. 169-177, 2009. · Zbl 1222.40004
[25] M. Mursaleen and S. A. Mohiuddine, “Almost bounded variation of double sequences and some four dimensional summability matrices,” Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 495-508, 2009. · Zbl 1212.40010
[26] M. Mursaleen and S. A. Mohiuddine, “Some inequalities on sublinear functionals related to the invariant mean for double sequences,” Mathematical Inequalities & Applications, vol. 13, no. 1, pp. 157-163, 2010. · Zbl 1189.40004 · doi:10.7153/mia-13-12 · http://files.ele-math.com/abstracts/mia-13-12-abs.pdf
[27] M. Mursaleen and S. A. Mohiuddine, “Invariant mean and some core theorems for double sequences,” Taiwanese Journal of Mathematics, vol. 14, no. 1, pp. 21-33, 2010. · Zbl 1209.40003
[28] M. Mursaleen and S. A. Mohiuddine, “Some matrix transformations of convex and paranormed sequence spaces into the spaces of invariant means,” Journal of Function Spaces and Applications, vol. 2012, Article ID 612671, 10 pages, 2012. · Zbl 1257.40001 · doi:10.1155/2012/612671
[29] M. Mursaleen and S. A. Mohiuddine, “Banach limit and some new spaces of double sequences,” Turkish Journal of Mathematics, vol. 36, no. 1, pp. 121-130, 2012. · Zbl 1248.46006
[30] M. Zeltser, M. Mursaleen, and S. A. Mohiuddine, “On almost conservative matrix methods for double sequence spaces,” Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 387-399, 2009. · Zbl 1212.40009
[31] G. A. Anastassiou, M. Mursaleen, and S. A. Mohiuddine, “Some approximation theorems for functions of two variables through almost convergence of double sequences,” Journal of Computational Analysis and Applications, vol. 13, no. 1, pp. 37-46, 2011. · Zbl 1222.41007
[32] B. Altay and F. Ba\csar, “Some new spaces of double sequences,” Journal of Mathematical Analysis and Applications, vol. 309, no. 1, pp. 70-90, 2005. · Zbl 1093.46004 · doi:10.1016/j.jmaa.2004.12.020