On second $\kappa$-variation

We present the notion of bounded second $\kappa$-variation for real functions defined on an interval $[a,b]$. We introduce the class $\kappa B{V}^2([a,b])$ of all functions of bounded second $\kappa$-variation on $[a,b]$. We show several properties of this class and present a sufficient condition under which a composition operator acts between these spaces.