On statistical convergence with respect to power series methods

Unver M., Bayram N. S.

POSITIVITY, cilt.26, sa.3, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s11117-022-00921-1
  • Dergi Adı: POSITIVITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: P-statistical convergence, P-strong convergence, Summability function, FK-topology, Weak convergence, POSITIVE LINEAR-OPERATORS, APPROXIMATION, SUMMABILITY, THEOREMS, SEQUENCE
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we establish a relationship between the concepts of P-strong, P-statistical convergences and P-uniform integrability where P stands for a power series method. We also prove that if a power series method has a summability function, then the space of all P-statistically convergent sequences cannot be endowed with a local convex FK-topology. We finally study P-statistical convergence in a Hausdorff topological space and investigate the relationships among these concepts and weak convergence of Baire measures.