@article{Li2025, 
author = {Qian Li and Zhouping Yin and Yuxin Wang and Qi Liu and Hongmei Zhang},
title = {A new constant in Banach spaces based on the Zb             a      ˇ      ganu constant        C          Z        (  B  )},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6480-6491},
keywords = {geometric constants, Banach space, Zbǎganu constant, ultrapower space, normal structure},
url = {https://www.sciopen.com/article/10.3934/math.2025296},
doi = {10.3934/math.2025296},
abstract = {In Banach spaces, first we present a new geometric constant,        C          Z              (      q      )        (  t  ,  B  ), which is closely related to the Zb             a      ˇ      ganu constant. We prove that              (      t      +      2              )                  q                                    2                  q          −          1                            (                              2                          q              −              1                                +                      t                          q                                      )             and        4    3   are respectively the lower and upper bounds for        C          Z              (      q      )        (  t  ,  B  ). Furthermore, we also derive that        C          Z              (      q      )        (  t  ,  B  )  =      C          Z              (      q      )        (  t  ,            B      ~        ), where              B      ~       denotes the ultrapower spaces of    B. Then, we can establish certain sufficient conditions that ensure a Banach spaces possesses a normal structure, which involve different constants such as the Zb             a      ˇ      ganu constant and Domínguez–Benavides coefficient.}
}