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

Abstract

The basis of our considerations is a characterization of Baire class one functions presented by Pen-Yee Lee, Wee-Kee Tang, Doingsheng Zhao \cite{b1}. In the first part of this paper,  we will prove an analogous characterization for functions belonging to the class $B_1^{**}$. 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.