In this paper we give an affirmative answer to two conjectures on generalized (m, n)-Jordan derivations and generalized (m, n)-Jordan centralizers raised in [S. Ali and A. Fošner, On Generalized (m, n)-Derivations and Generalized (m, n)-Jordan Derivations in Rings, Algebra Colloq. 21 (2014), 411-420] and [A. Fošner, A note on generalized (m, n)-Jordan centralizers, Demonstratio Math. 46 (2013), 254-262]. Precisely, when R is a semiprime ring, we prove, under some suitable torsion restrictions, that every nonzero generalized (m, n)-Jordan derivation (resp., a generalized (m, n)-Jordan centralizer) is a derivation (resp., a two-sided centralizer).