Double-sided Taylors approximations and their applications in Theory of analytic inequalities

In this paper the double-sided Taylors approximations are studied. A short proof of a well-known theorem on the double-sided Taylors approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such approximations. Then we present some new applications of the double-sided Taylors approximations in the theory of analytic inequalities.