On bicomplex BC-modules l(p)(k) (BC) and some of their geometric properties

Değirmen N., Sağır Duyar B.

GEORGIAN MATHEMATICAL JOURNAL, vol.30, pp.65-79, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30
  • Publication Date: 2023
  • Doi Number: 10.1515/gmj-2022-2194
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.65-79
  • Keywords: Bicomplex power, D-normed Banach bicomplex BC-module, BC-convexity, BC-strict convexity, BC-uniform convexity, SPACES
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | center dot |l(k) and we discuss some topological and geometric concepts such as completeness, convexity, strict convexity and uniform convexity in the bicomplex setting with respect to the hyperbolic-valued norm. parallel to parallel to(D) by defining the concept of parallel to parallel to(D)-normed Banach bicomplex A-module and constructing..-normed Banach bicomplex BC-modules l(p)(k) (BC).