# Some aspects of generalized Zbăganu and James constant in Banach spaces

- Authors
- 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
- 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.