Bicomplex approach to double sequences

Değirmen N., GÜNGÖR N., Sagir B.

Maejo International Journal of Science and Technology, cilt.19, sa.3, ss.274-288, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 3
  • Basım Tarihi: 2025
  • Dergi Adı: Maejo International Journal of Science and Technology
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.274-288
  • Anahtar Kelimeler: bicomplex number, convergence in Pringsheim’s sense, double sequence, hyperbolic valued norm
  • Samsun Üniversitesi Adresli: Evet

Özet

In this study we introduce bicomplex versions of double sequences, extending the classical theory of sequences to the bicomplex number system. Also, we discuss formal definitions of bicomplex double sequences and investigate their fundamental properties pertaining to the hyperbolic valued norm |. |k which serves as a natural tool for measuring the magnitude of bicomplex numbers while preserving their algebraic characteristics. Furthermore, we give some examples to show the usability of our findings and applicability of the theoretical results. The findings offer a foundational contribution to bicomplex analysis with potential implications for functional analysis, operator theory and other areas of applied mathematics.