Generalized Limits and Statistical Convergence

YURDAKADİM T., Khan M., Miller H., Orhan C.

Mediterranean Journal of Mathematics, cilt.13, sa.3, ss.1135-1149, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00009-015-0554-y
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1135-1149
  • Anahtar Kelimeler: almost convergence, Banach limit, matrix summability, statistical convergence, statistical limit superior and inferior, The Hahn–Banach extension theorem
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Hayır

Özet

Consider the Banach space m of real bounded sequences, x, with ‖ x‖ = sup k| xk|. A positive linear functional L on m is called an S-limit if L(χK) = 0 for every characteristic sequence χK of sets, K, of natural density zero. We provide regular sublinear functionals that both generate as well as dominate S-limits. The paper also shows that the set of S-limits and the collection of Banach limits are distinct but their intersection is not empty. Furthermore, we show that the generalized limits generated by translative regular methods is equal to the set of Banach limits. Some applications are also provided.