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Article

Keywords:
statistical convergence; invariant means; core theorems; matrix transformations
Summary:
In [5] and [10], statistical-conservative and $\sigma $-conservative matrices were characterized. In this note we have determined a class of statistical and $\sigma $-conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
References:
[1] H. Çoşkun, C. Çakan and Mursaleen: On the statistical and $\sigma $-cores. Studia Math. 153 (2003), 29–35. MR 1949047
[2] G.  Das: Sublinear functionals and a class of conservative matrices. Bull. Inst. Math. Acad. Sinica 15 (1987), 89–106. MR 0947779 | Zbl 0632.46008
[3] J. A.  Fridy and C.  Orhan: Statistical limit superior and limit inferior. Proc. Amer. Math. Soc. 125 (1997), 3625–3631. DOI 10.1090/S0002-9939-97-04000-8 | MR 1416085
[4] J.  Li and J. A.  Fridy: Matrix transformations of statistical cores of complex sequences. Analysis 20 (2000), 15–34. MR 1757066
[5] E.  Kolk: Matrix maps into the space of statistically convergent bounded sequences. Proc. Estonian Acad. Sci. Phys. Math. 45 (1996), 187–192. MR 1426169 | Zbl 0865.40001
[6] I. J.  Maddox: Elements of Functional Analysis. Cambridge University Press, Cambridge, 1970. MR 0390692 | Zbl 0193.08601
[7] S. L.  Mishra, B.  Satapathy and N.  Rath: Invariant means and $\sigma $-core. J.  Indian Math. Soc. 60 (1984), 151–158. MR 1292133
[8] Mursaleen: On some new invariant matrix methods of summability. Quart. J.  Math. Oxford Ser.  2 34 (1983), 77–86. DOI 10.1093/qmath/34.1.77 | MR 0688425 | Zbl 0539.40006
[9] R.  Raimi: Invariant means and invariant matrix methods of summability. Duke Math.  J. 30 (1963), 81–94. DOI 10.1215/S0012-7094-63-03009-6 | MR 0154005 | Zbl 0125.03201
[10] P.  Schaefer: Infinite matrices and invariant means. Proc. Amer. Math. Soc. 36 (1972), 104–110. DOI 10.1090/S0002-9939-1972-0306763-0 | MR 0306763 | Zbl 0255.40003
[11] S.  Simons: Banach limits, infinite matrices and sublinear functionals. J.  Math. Anal. Appl. 26 (1969), 640–655. DOI 10.1016/0022-247X(69)90203-0 | MR 0241957 | Zbl 0176.46001
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