@article{Voloshyn_Maslyuchenko_Nesterenko_2012, title={On approximation of mappings with values in the space of continuous functions: Array}, volume={4}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/2400}, abstractNote={<p>Using a theorem on the approximation of the identity in the Banach space $C_u(Y)$ of all continuous functions $g: Y\rightarrow \mathbb{R}$, defined on a metrizable compact $Y$ with the uniform norm, we prove that for a topological space $X$, a metrizable compact $Y$, a linear subspace $L$ of $Y$ dense in $C_u(Y)$ and a separately continuous function $f: X\times Y\rightarrow \mathbb{R}$ there exists a sequence of jointly continuous functions $f_n: X\times Y\rightarrow \mathbb{R}$ such that $f_n^x = f(x, \cdot)\in L$ and $f_n^x \rightarrow f^x$ in $C_u(Y)$ for each $x\in X$.</p>}, number={1}, journal={Carpathian Mathematical Publications}, author={Voloshyn, H.A. and Maslyuchenko, V.K. and Nesterenko, O.N.}, year={2012}, month={Jun.}, pages={23–27} }