Maximum $m-cv$ and $m-psh$ functions

The $m$-convex functions, $(m-cv)$ and the $m$-plurisubharmonic functions $(m-psh)$ are the real analogue in ${{\mathbb{R}}^{n}}$ of strongly $m$-subharmonic $(s{{h}_{m}})$ functions in the complex space ${{\mathbb{C}}^{n}}.$ In the report we will establish one very useful connection between $(m-cv)$ and $(s{{h}_{m}})$ functions. Next, using the rich properties of $(s{{h}_{m}})$ functions, we will study $(m-cv)$ and $(m-psh)$ functions.