We prove, among other results, that $min(u,v)$ is plurisubharmonic (psh) when $u,v$ belong to a family of functions in $\mathrm{psh}\left(D\right)\cap {\Lambda }_{\alpha }\left(D\right),$ where ${\Lambda }_{\alpha }\left(D\right)$ is the $\alpha$-Lipchitz functional space with $1<\alpha <2.$ Then we establish a new characterization of holomorphic functions defined on open sets of ${ℂ}^n.$