On geometrical characteristics and inequalities of new bicomplex Lebesgue Spaces with hyperbolic-valued norm

Toksoy E., Sagir B.

GEORGIAN MATHEMATICAL JOURNAL, cilt.31, sa.3, ss.483-495, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/gmj-2023-2093
  • Dergi Adı: GEORGIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.483-495
  • Anahtar Kelimeler: Bicomplex Lebesgue space
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this work, it is assumed that the norm over bicomplex numbers is the hyperbolic ( D -valued) norm. In this paper, we provide an overview of bicomplex Lebesgue spaces and investigate some of their geometric properties, including BC-convexity, BC -strict convexity, and BC -uniform convexity. Moreover, the basic inequalities such as D-Holder's inequality and D -Minkowski inequality for bicomplex Lebesgue spaces are presented, used to show geometric properties.