Characterization of generalized absolute Cesàro summability factors

Abstract

Recently, Sarıgöl (in: Kuwait J Sci 42(3):28–35, 2015) has investigated the summability factors of type \(\varepsilon \in \left( {\left| {C,\alpha } \right|_{k} ,\left| {\bar{N}, p_{n} } \right|} \right)\), for \(\alpha > - 1\), \(k > 1\) and arbitrary positive sequence \(\left( {p_{n} } \right)\), which extends some well known results. The aim of this paper is to generalize these results using more general summability \(\left| {C,\alpha ,\beta } \right|_{k}\), \(k \ge 1.\) More precisely, we give characterization of the summability factors of the types \(\left( {\left| {C,\alpha ,\beta } \right|_{k} ,\left| {\bar{N}, p_{n} } \right|} \right)\), \(k > 1\) and \(\left( {\left| {\bar{N}, p_{n} } \right|,\left| {C,\alpha ,\beta } \right|_{k} } \right) , k \ge 1\) for \(\alpha + \beta > - 1\) and a positive sequence \(\left( {p_{n} } \right)\).

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Correspondence to G. Canan Hazar Güleç.

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Hazar Güleç, G.C. Characterization of generalized absolute Cesàro summability factors. J Anal (2020). https://doi.org/10.1007/s41478-020-00249-7

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Keywords

  • Generalized absolute Cesàro summability
  • Summability factors
  • Inclusion relations

Mathematics Subject Classification

  • 40C05
  • 40D25
  • 40F05
  • 46A45