ASYMPTOTIC DOUBLE SUBSERIES

Patterson R. F., Srivastava H., SAVAŞ E.

Publications de l'Institut Mathematique, vol.112, no.126, pp.143-150, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 112 Issue: 126
  • Publication Date: 2022
  • Doi Number: 10.2298/pim2226143p
  • Journal Name: Publications de l'Institut Mathematique
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Page Numbers: pp.143-150
  • Keywords: Double sequences, Double subseries, P-convergent
  • Uşak University Affiliated: Yes

Abstract

In 1964 Šalát presented a notion of asymptotic density of single dimensional subseries. Using this notion he presented a series of theorems similar to the following. If dn be a decreasing sequence such that (Formula Presented) and let the subseries (Formula Presented) of the series (Formula Presented) be convergent, then (Formula Presented). Following Šalát’s patten, we present a notion of double subseries and a natural variation of Šalát’s theorem.