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This monograph is part of the field approximation theory, which covers a great deal of mathematical territory. The focus is dedicated to presenting various qualitative and quantitative versions of Voronovskaja's type theorem applied for a large class of linear positive operators. Such issues have attracted the attention of thousands mathematicians in the last 80 years. Using this method we get the asymptotic behavior, the uniform convergence and the approximation order of the approximated functions for many well-known linear positive operators. It is interesting the fact that, we get some new and old results without using Popoviciu-Bohman-Korovkin's theorem for the convergence of a linear positive operator towards the identity operator or the O. Shisha and B. Mond result for the estimate of the approximation order.