Skew generalized von Neumann-Jordan constant for the Bana\'s-Fr\k{a}czek space

For any $\lambda>1, R_\lambda^2$ is Bana\'s-Fr\k{a}czek space, the exact value of the skew generalized von Neumann-Jordan constant $C_{\mathrm{NJ}}^p\left(\xi, \eta, R_\lambda^2\right)$ is calculated. By careful calculations, $C_{\mathrm{NJ}}^p\left(\xi, \eta, R_\lambda^2\right)=\frac{(\xi+\eta)^p+\left[(\eta+\xi)^2-\frac{4 \xi \eta}{\lambda^2}\right]^{p / 2}}{2^{p-1}\left(\xi^p+\eta^p\right)}$ is given.