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Fo\\v{s}ner, \\textit{On Generalized $(m, n)$-Derivations and Generalized $(m, n)$-Jordan Derivations in Rings,} Algebra Colloq. \\textbf{21} (2014), 411--420] and [A. Fo\\v{s}ner, \\textit{A note on generalized $(m,n)$-Jordan centralizers,} Demonstratio Math. \\textbf{46} (2013), 254--262]. 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