Equi-Baire one family of functions on metric spaces: A generalization of equi-continuity; and some applications

A survey on composition operators on some function spaces

“…For example, semi-continuous functions and derived functions, all belong to this class ( [12,22]). Some interesting, very recent results concerning fixed points of Baire functions and the so called equi-Baire property can be found in [1] and [2].…”

A survey on composition operators on some function spaces

“…This last property is not a characterisation as the following example shows ( [38]: page 148, Example IV). Interesting very recent results concerning fixed points of Baire functions and the so called equi-Baire property are in [1] and [2].…”

Equi-Baire 1 families of functions

“…The notion of equi-Baire 1 families of functions introduced by Lecomte [15] and rediscovered by Alikhani-Koopaei [1] was motivated by the epsilon-delta characterization of Baire 1 functions due to Lee, Tang and Zhao [17]. Another old characterization of Baire 1 functions, due to Lebesgue [14], turns out useful in this context since, in some general cases, equi-Baire 1 families coincide with equi-Lebesgue ones.…”

“…Another old characterization of Baire 1 functions, due to Lebesgue [14], turns out useful in this context since, in some general cases, equi-Baire 1 families coincide with equi-Lebesgue ones. The notion of equi-Lebesgue family is introduced in our paper, however it appeared without this name in [15,Proposition 32] and [1,Theorem 3.6]).…”