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

Toksoy E., Sagir B.

GEORGIAN MATHEMATICAL JOURNAL, vol.31, no.3, pp.483-495, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1515/gmj-2023-2093
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.483-495
  • Keywords: Bicomplex Lebesgue space
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.