Lacunary Distributional Convergence in Topological Spaces

Creative Commons License

Uluçay H., ÜNVER M.

FILOMAT, cilt.33, sa.13, ss.4297-4306, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 13
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/fil1913297u
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4297-4306
  • Anahtar Kelimeler: Distributional convergence, statistical convergence, lacunary sequence, STATISTICAL CONVERGENCE, SUMMABILITY
  • Ankara Üniversitesi Adresli: Evet

Özet

Most of the summability methods cannot be defined in an arbitrary Hausdorff topological space unless one introduces a linear or a group structure. In the present paper, using distribution functions over the Borel sigma-field of the topology and lacunary sequences we define a new type of convergence method in an arbitrary Hausdorff topological space and we study some inclusion theorems with respect to the resulting summability method. We also investigate the inclusion relation between lacunary sequence and lacunary refinement of it.