Tauberian Theorems for Sequences in 2-Normed Spaces

Savaş R. , Sezer S. A.

RESULTS IN MATHEMATICS, vol.72, pp.1919-1931, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72
  • Publication Date: 2017
  • Doi Number: 10.1007/s00025-017-0747-8
  • Title of Journal : RESULTS IN MATHEMATICS
  • Page Numbers: pp.1919-1931
  • Keywords: Tauberian theorems, 2-normed spaces, slowly oscillating sequences, two-sided Tauberian conditions, STATISTICAL CONVERGENCE, CESARO SUMMABILITY, IDEAL CONVERGENCE

Abstract

In this paper we initiate the study of Tauberian theorems for sequences in 2-normed spaces. We introduce a necessary and sufficient Tauberian condition for (C, 1) summable sequences in such spaces. Corollaries allow this condition to be replaced by 2-normed analogues of Schmidt-type slow oscillation condition or Hardy-type two-sided condition.