Gámez Merino, José LuisMendoza Casas, José2023-06-202023-06-2019980039-3223https://hdl.handle.net/20.500.14352/57301The two main results of this paper are the following: (a) If X is a Banach space and f : [a, b] --> X is a function such that x*f is Denjoy integrable for all x* is an element of X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function f : [a, b] --> c(0) which is not Pettis integrable on any subinterval in [a, b], while integral(J)f belongs to co for every subinterval J in [a, b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dunford and Denjoy-Pettis integrals are studied.engjournal articlehttps://bit.ly/2IoNmoqhttp://www.icm.edu.pl/restricted access517.986.6517.518.45Banach-valued functionsDenjoy-Dunford integralsDenjoy-Pettis integralsAnálisis matemático1202 Análisis y Análisis Funcional