(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2017)
Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! R be an (; )-derivation. In the present paper we discuss the following situations: (i) F(xoy) = a(xy yx), (ii) F([x; y]) = a(xy yx), (iii) d(x)od(y) = a(xy yx) for all x; y 2 and a 2 f0; 1;ô€€€1g. Also some related results have been obtained.