A-Statistical Convergence with a Rate and Applications to Approximation

GÜLFIRAT M.

Filomat, cilt.36, sa.15, ss.5323-5335, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 15
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2215323g
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.5323-5335
  • Anahtar Kelimeler: Subject Classification, Density, Statistical convergence, Uniform integrability, Strong convergence, Distributional convergence, Korovkin type approximation, SUMMABILITY
  • Ankara Üniversitesi Adresli: Evet

Özet

A = (ank) be a regular summability matrix. In the present paper we deal with subspaces of the space of A−statistically convergent sequences obtained by the rate at which the A−statistical limit tends to zero. We prove that a sequence is the A−strongly convergent if and only if it is the A−statistically convergent and the A−uniformly integrable with the rate of o (an ) where a = (an ) is a positive nonincreasing sequence. We also make a link between the A−strong convergence and the A−distributional convergence with the rate of o (an ). Finally, as an application we present an approximation theorem of Korovkin type.