Tauberian conditions under which statistical convergence follows from statistical summability by weighted means

Moricz F., Orhan C.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.41, no.4, pp.391-403, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2004
  • Doi Number: 10.1556/sscmath.41.2004.4.3
  • Journal Name: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.391-403
  • Keywords: statistical convergence, statistical summability (N,p), statistical limit inferior, statistical limit superior, one-sided and two-sided Tauberian conditions, slow decrease, slow oscillation
  • Ankara University Affiliated: No

Abstract

The first named author has recently proved necessary and sufficient Tauberian conditions under which statistical convergence (introduced by H. Fast in 1951) follows from statistical summability (C, 1). The aim of the present paper is to generalize these results to a large class of summability methods (N,p) by weighted means.