# zbMATH — the first resource for mathematics

Generalized almost convergence and Knopp’s core theorem. (English) Zbl 0892.40005
In [J. Math. Anal. Appl. 132, No. 1, 226-233 (1988; Zbl 0648.40004)], B. Choudhary has extended the well-known Knopp core theorem. The purpose of this paper is to generalize the results due to M. Stieglitz [Math. Japonicae 18, 53-70 (1973; Zbl 0279.40003)] by using the concept of $$E_{\mathcal B}$$-convergence.

##### MSC:
 40C05 Matrix methods for summability 40J05 Summability in abstract structures 46A45 Sequence spaces (including Köthe sequence spaces)
Full Text:
##### References:
 [1] CHOUDHARY B.: An extension of Knopp’s core theorem. J. Math. Anal. Appl. 132 (1988), 226-233. · Zbl 0648.40004 [2] DAS G.: Sublinear functionals and a class of conservative matrices. Bull. Inst. Math. Acad. Sinica 15 (1987), 89-106. · Zbl 0632.46008 [3] DEVI S. L.: Banach limits and infinite matrices. J. London Math. Soc. 12 (1976), 397-401. · Zbl 0321.46009 [4] KUTTNER B.-MADDOX I. J.: Inequalities between functionals on bounded sequences. Indian J. Math. 2 (1983), 1-10. · Zbl 0576.40003 [5] LORENTZ G. G.: A contribution to the theory of divergent sequences. Acta Math. 80 (1948), 167-190. · Zbl 0031.29501 [6] ORHAN C.: Sublinear functionals and Knopp’s core theorem. Internat. J. Math. Math. Sci. 13 (1990), 461-468. · Zbl 0717.40013 [7] STIEGLITZ M.: Eine Verallgenmeinerung des Begriffs Fastkonvergenz. Math. Japon. 18 (1973), 53-70. · Zbl 0279.40003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.