On the $L_{\mathrm{YJ}}(\xi, \eta, X)$ constant for the Bana\'s-Fr\k{a}czek space

Abstract

In this paper, for any $\lambda \geq 1, R_\lambda^2$ is the Bana\'s-Fr\k{a}czek space. The exact value of $L_{\mathrm{YJ}}(\xi, \eta, X)$ for this space will be calculated. Specifically, $L_{\mathrm{YJ}}\left(\xi, \eta, R_\lambda^2\right)=1+\frac{2 \xi \eta}{\xi^2+\eta^2}\left(1-\frac{1}{\lambda^2}\right)$ is the result thereafter through meticilous computation.