On approximation of the separately and jointly continuous functions

On approximation of the separately and jointly continuous functions}%{We investigate the following problem: which dense subspaces$L$ of the Banach space $C(Y)$ of continuous functions on acompact $Y$ and topological spaces $X$ have such property, thatfor every separately or jointly continuous functions $f: Ximes Yightarrow mathbb{R}$ there exists a sequence of separately orjointly continuous functions $f_{n}: Ximes Y ightarrowmathbb{R}$ such, that $f_n^x=f_n(x, cdot) in L$ for arbitrary $nin mathbb{N}$, $xin X$ and $f_n^xightrightarrows f^x$ on $Y$ for every $xin X$? In particular, it was shown, if the space $C(Y)$ has a basis that every jointly continuous function $f: Ximes Y ightarrow mathbb{R}$ has jointly continuous approximations $f_n$ such type.