New results in gradual normed linear spaces in light of generalized statistical convergence via ideal

SAVAŞ E., Kişi Ö., Choudhury C.

Filomat, vol.38, no.15, pp.5399-5413, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 15
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2415399s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5399-5413
  • Keywords: gradual normed linear space, Gradual number, Ir,α st (G)−limit set, I−statistical convergence, rough convergence
  • Uşak University Affiliated: Yes

Abstract

This article introduces the novel concept of rough I−statistical convergence of order α in gradual normed linear spaces (GNLS). The paper presents noteworthy findings utilizing the Ir,α st (G)− limit set, which exhibits several fundamental properties of the concept. Moreover, a necessary and sufficient condition for (G)−convergence of a sequence in a GNLS is established. Ir,α st.