Affordable Access

Access to the full text

Some aspects of generalized Zbăganu and James constant in Banach spaces

Authors
  • Liu, Qi1
  • Sarfraz, Muhammad1
  • Li, Yongjin1
  • 1 Department of Mathematics, Sun Yat-sen University, 510275 , (China)
Type
Published Article
Journal
Demonstratio Mathematica
Publisher
De Gruyter
Publication Date
Aug 16, 2021
Volume
54
Issue
1
Pages
299–310
Identifiers
DOI: 10.1515/dema-2021-0033
Source
De Gruyter
Keywords
Disciplines
  • Research Article
License
Green

Abstract

We shall introduce a new geometric constant C Z ( λ , μ , X ) {C}_{Z}\left(\lambda ,\mu ,X) based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. First, it is shown that, for a Banach space, C Z ( λ , μ , X ) {C}_{Z}\left(\lambda ,\mu ,X) is equal to 1 if and only if the norm is induced by an inner product. Next, a characterization of uniformly non-square is given, that is, X X has the fixed point property. Also, a sufficient condition which implies weak normal structure is presented. Moreover, a generalized James constant J ( λ , X ) J\left(\lambda ,X) is also introduced. Finally, some basic properties of this new coefficient are presented.

Report this publication

Statistics

Seen <100 times