Scalar derivatives were introduced for characterization of monotone operators (in sense of Minty-Browder) which are an important tool for solving operator equations, variational inequalities, complementarity problems and partial differential equations. The asymptotic version of the scalar derivative was defined by G. Isac for generalizing a classical fixed point theorem of Krasnoselskii. The scalar asymptotic derivatives generalize the asymptotic derivatives used by Krasnoselskii in his theorem. By introducing the notion of the inversion of a mapping a kind of duality between the scalar derivatives and the scalar asymptotic derivatives will be obtained. This duality will be used for finding scalar asymptotic derivatives of a mapping which in general are not asymptotic derivatives. Replacing assumption 3. of Theorem 3.1 of Isac by these expressions of the scalar asymptotic derivatives various fixed point theorems will be generated. These fixed point theorems will be used for generating surjectivity theorems, solving variational inequalities, complementarity problems and integral equations.