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An Application of Absolute Matrix Summability using Almost Increasing and delta-quasi-monotone Sequences

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In the present paper, absolute matrix summability of in finite series is studied. A new theorem concerning absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of in finite series, is proved using almost increasing and -quasi-monotone sequences. Also, a result dealing with absolute Ces aro summability is given.

Abstract

In the present paper, absolute matrix summability of in finite series is studied. A new theorem concerning absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of in finite series, is proved using almost increasing and -quasi-monotone sequences. Also, a result dealing with absolute Ces aro summability is given.

참고문헌 (9)

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  3. H. Bor, "On two summability methods", Math. Proc. Cambridge Philos. Soc, 97, pp.147~149 (1985)
  4. H. Bor, "An application of almost increasing and δ-quasi-monotone sequences", JIPAM. J. Inequal. Pure Appl. Math, 1(2), pp.6~ (2000)
  5. H. Bor, "Corrigendum on the paper "An application of almost increasing and δ-quasimonotone sequences"", JIPAM. J. Inequal. Pure Appl. Math, 3(1), pp.2~ (2002)
  6. T. M. Flett, "On an extension of absolute summability and some theorems of Littlewood and Paley", Proc. London Math. Soc, 7, pp.113~141 (1957)
  7. G. H. Hardy, "Divergent Series" (1949), Oxford University Press
  8. E. Kogbetliantz, "Sur les series absolument sommables par la methode des moyennes arithmetiques", Bull. Sci. Math, 49, pp.234~256 (1925)
  9. W. T. Sulaiman, "Inclusion theorems for absolute matrix summability methods of an infinite series. IV", Indian J. Pure Appl. Math, 34(11), pp.1547~1557 (2003)

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