Generalized Limits and Statistical Convergence

Yurdakadim T., Khan M. K., Miller H. I., Orhan C.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.13, sa.3, ss.1135-1149, 2016 (SCI-Expanded, Scopus) identifier 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: The Hahn-Banach extension theorem, Banach limit, almost convergence, statistical convergence, statistical limit superior and inferior, matrix summability, SEQUENCES, SUMMABILITY, SPACES
  • Ankara Üniversitesi Adresli: Evet

Özet

Consider the Banach space m of real bounded sequences, x, with . A positive linear functional L on m is called an S-limit if for every characteristic sequence 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.