On some characterizations of Baire class one functions and Baire class one like functions

The basis of our considerations is a characterization of Baire class one functions presented by [Pen-Yee Lee - Wee-Kee Tang - Doingsheng Zhao: An equivalent definition of functions of the first Baire class, in: Proc. Amer. Math. Soc., Vol. 129, 2000, pp. 2273-2275]. In the first part of this paper, we will prove an analogous characterization for functions belonging to the class . In the last part, we will consider various classes of functions connected with the characterization mentioned above, which permits to give a new characterization of Baire class one functions.